Regarding the phono output, if there is a switch I could use to activate it, rather than have to unplug the headphones, i could get used to that I think. I would however want it to be a fixed volume that is not controlled by the DAC/AMP itself. This is what put me off the FiiO K5 PRO.
Just note that the lower range AudioGDs may need to have some jumper in the board or have the jumpers removed for the output to function one way or another and only have three positions on the switch to sort of make it clearer what it will do or something like that. Not all of them but there are a few of them who need those jumpers in there or out depending on what you need, just consult the manual first. Don't worry you only need a screwdriver and, at worst, I think a tweezer.
Speaking of the K5 pro, that is easily within my budget, and I assume it will be far more powerful than my A3. But based on the information you are giving, with such high impedance headphones, I am assuming even this won't seem all that much better at driving the 600ohm DT880s?
Sort of. But when I pointed out that you shouldn't underestimate how much power you need due to the logarithmic relationship between iinput power and actual loudness, I was talking about power in general, not the K5 Pro in particular.
As for the K5 Pro in particular...it's way more powerful than the A3. At 32ohms. It has 1500mW (1.5watts) per channel if it gets a 32ohm load. This is where you might have a problem: it doesn't state anywhere on the product page what its output power is at 300ohm/600ohms. Some amps can have output power drop faster than other amps' when the load impedance is increased, so it's not impossible that it might have less than 150mW into a 300ohm load, and way under 100mW into a 600ohm load.
To be fair that's still a lot more than what the A3 puts out, but given how you're paying more for connectivity features than power nowadays, it's not hard to find something that has both connectivity options and a heck lot more power (that can come in handy if you get lower sensitivity headphones in the future) for not a lot more money.
I still wonder what my Pioneer A-209R has in it, as it is intended for speakers, has numerous inputs and the headphone output delivers more power than the DT880s would ever need even before the volume knob is half way. This amplifier cost £139 and most of the features in it are not for headphones. The things is misses out on is any digital inputs at all.
Maybe it's still like the older integrated amps that use the actual amplifier output stage to drive the headphone output and is just routed through there via some kind of switch unlike some amps since the late 1980s that just have some daughterboard with a headphone driver chip that has a high output impedance. Like how a Marantz CDP has the same daughterboard behind the headphone jack as a Marantz integrated amp, so if you were only using headphones, it doesn't make sense getting the integrated amp.
Or maybe it actually does have a daughterboard with a Philips chip, like on Marantz, which is actually a fairly good chip. At least in the sense that my Marantz CD60 sounds louder and a heck of a lot better than plugging my HD600 into my NAD304's headphone jack (that really, really sucked - unlike plugging Stax headphones with that voltage converter thing via the speaker binding posts). Well...not just up to that good...Fiio used a slightly modified version of that Philips headphone driver chip from 1989 on the original E9 and then an even newer version on the E09K.
So not really all that powerful, but compared to your A3, it is. It might even be piling more distortion at your listening level on that integrated amp than a good headphone amp would, but no way to tell without my listening to the same Pioneer and even then I can't guarantee if you would be able to hear the difference.
According to the specs it has 250mW into 300ohms.
So still more powerful than the A3, but I'm not sure if it's more power than the AudioGD at 600ohms, or how much more distortion it has.
However I had been assuming you had the 250ohm version. Since you have the 600ohm version, gimmeheadroom's suggestion to go with an OTL amp is a better if highly solution, if highly specific to that particular headphone (and other 600ohm headphones, which would be the T1 since I don't think anybody else makes 600ohm headphones anymore).
On the flipside if that integrated amp - which is from a series most known for being the music store choice for in-store demos than for actually being loved by audiophiles - gets loud enough for you then maybe the AudioGD or that Topping could still be loud enough, except for one thing: one factor there might be gain. Integrated amps tend to have higehr gain compared to most headphone amps (since headphones can more easily have audible noise given the drivers' proximity to your ears), save for a few that have a really high high gain setting. Price aside the AudioGD has its gain settings on the specs, but I can't see that for the Topping, so the AudioGD might be a safer bet short of just going with an OTL amp.
My other cheaper option may be to keep using my M3 (which probably isn't the best DAC)...
I use my Hidizs AP80 as a music player via the line out into my Meier Cantate.2. It has a 2V line output setting, so basically the same voltage as a CDP, unlike older DAPs that have more powerful headphone driver stages built more like a miniature CDP but the line outputs are only 1.2V. Your M6 has a setting for that too. Both aren't exactly like a CDP/DAC output stage as the setting is there (and not as a separate output port) because on these newer integrated audio chips (DAC+headphone driver chips; note that there isn't a real equivalent to a line output stage that is the most complex relative to how these chips are built) what the setting really does is just cap the otherwise variable output to the level where the output would be equivalent to 2V.
Basically though unless you're using the most esoteric equipment this is fine. Hell even the iPod's 1.2V simplified line output circuit sounded really good, it's only bested by CDPs/DACs that have better imaging (and TTs+phono stages) and when such sources are paired with an amp that would already be piling on noise when you crank it up more to compensate for the lower output voltage out of the iPod. This is why you can find people with really expensive gear claiming the iPod sounds the same as midrange CDPs if not the best source units, but there are some people with amps that aren't exactly the most magical (but, like, still have a dedicated listening room and great speakers) who can hear a difference between the iPod and their CDP. I couldn't hear the difference on a Krell system but I could on NAD and Marantz, I just didn't think like some skeptics who just think it's all bull or that the NAD and Marantz are "more transparent," I just think maybe I'm pushing a 35wpc NAD304 (let alone a PM80 I kept in Class A mode) straight into the distortion zone (it was outright clipping on the Marantz) when the source signal is only 1.2V.
...and use a very powerful headphone amplifier that just has a phono input. Maybe you could let me know about some of these options.
If you're open to this option and want to try an approach more specific to the DT880/600 (vs lower impedance, lower sensitivity headphones), then an OTL headphone amp is your best bet for getting power into a 600ohm headphone.
If you want some kind of flexibility with other headphones, there's the Schiit Asgard3 and Lyr3. Asgard will give you 300mW into 600ohms - it costs well under what the AudioGD costs and gets you a better amp (though not full Class A operation, just has a lot of Class A bias).
One downside to these though: their line outputs are controlled by the preamp. This is actually the more common thing for headphone amps and even DAC-HPamps-Preamps because the assumption is that if you have a headphone amp it's more likely you'll be using active desktop speakers followed by just using a pure power amp and using the HPA/DAC-HPA-Preamp as the main hub/preamp, and using integrated amps with HPAs is still more commonly done via the Rec Out on the integrated amps. No it's not very common for there to be any interference...so if your Pioneer has it, well, that's kind of why it's more known as the music store demo unit.
Passthrough on pure HPAs is mostly on older HPAs, and in the case of the AudioGD, they're out of space and just bet that if you're gonna upgrade the thing, it's far more likely you'd need to upgrade it because you need more power to drive a headphone, so they're the optional fixed level output because headphone amps don't come as separate preamp and pure amp boxes. if one comes in two boxes, the other unit is the power supply (or a desktop battery pack as on the more esoteric products), often in the same chassis as the amp (ex the WooAudio WA6se).
I have to say I love the look and design of the amplifier you have pics of, but that seems to only really be available in the USA.
AudioGD? They're made in China and the website has instructions on how to order from the US, EU, or anywhere else. And thanks to the Orange Overlord (and his replacement), these are punitively taxed in the US, so them being from China gets them a tax rate similar to what the EU would. But only because they're made in China.
Schiit though...those are made in the US. They have an EU distributor but throughout the human malware situation I've only ever seen people claiming the EU distributor doesn't have anything. If you're in the UK or Ireland, I'm not sure if there's already a separate UK dealer.
if you are in the EU and you can go with just an amp and no built in DAC, there's Meier Audio in Germany.
Still, there's the problem with how you want to hook things up because if these have any line outputs, they're preamp outputs.