My 2 cents:
Purely about the 400i - I have listened to them extensively from Cayin C5 (very nice), Xduoo XD05 (superb) and iFi iCan SE + Loki (good). Plenty of times I get lost in the music, they are a lovely set of headphones to listen to, especially when paired with the right amp. I listen to them indoors and outdoors. Honestly, I love them. There is plenty of detail but never at the expense of the listening experience. I listen to a very wide range of music BUT I am also 48 and potentially not as able to hear high frequencies as you (though I personally think I'm doing ok!)
I bought them without auditioning them (usually I audition) because the price was so good. I have only been VERY pleased I did!
First of all thanks for the help both of you, good to hear that you can get a good experience with the music without much problem with the details. Those amps you mentioned, they tend to a more warm output?
You have an interesting question and this is my impression between the HE400i, HD650/HD6XX, HD660S, HD598 and SHP9500. Keep in mind that some of this is from memory since I have given away my SHP9500 and HD598, modded my HE400i and only listened to the HD660S 5 times over a 6 month period.
SHP9500: it was a bit bright with a dry/lean overall sound that I didn't care for and different amps/DACs made no difference to me
HD598: one of the first "better" headphones that I got but once I listened to others like HE400 and HD650 I knew that they were not what I prefer. They are great headphones for the price and in some ways like sound stage and no mid-bass bump better than the HD650/6XX and HD600.
If you don't want to deal with amps then I suggest the HD660S, a bit over priced but since no amp is really needed its something to be considered but since I have a decent OTL amp (BH Crack) my HD650 and HD6XX do sound a touch better than the HD660S to me so I'll wait for the price of the HD660S to go down to $300 or under before I'd consider buying them.
HD650/6XX: both can be a bit too warm for some but with a proper amp they are the smoothest and easiest to listen to along with being forgiving of poorly recorded tracks
HE400i: aside from the QC issues with broken yokes they are not bad out of a phone or DAP but benefit a slightly warm SS or hybrid amp, a little more detailed and no rolled of highs like the HD650/6XX but for some they can be harsh at times. Another thing to consider is that the current version with the 2.5mm jacks sounds a little different that the older SMC jack version.
Since you didn't say what your music preferences are its hard to give a better suggestion but a few other headphones that might interest you: HD700, Grado SR225e (change the ear pads to G-cush), HE560 (can get them fairly cheap but they also have issue with the yoke breaking like the HE400i), Sundara, and EL-8 open (being discontinued so they are quite cheap these days).
I think this is important: I'm kinda sensitive to treble, not so much tho. I can get fatigue on some songs with the SHP9500, do you think if the Hifiman has even more treble fatiguing potential?
I'd love to buy more expensive headphones like the Sundara but by max budget is limited to 200 dollars (which means I can't buy a expensive amp right now, I'm leaning towards the FX-audio Dac X6 which is kinda warm), I don't have problem buying used cans as well.
I listen to so much different stuff, but mostly Rock (from indie rock to post-punk or even classical rock from Beatles to Fleetwood Mac), I don't really like metal or it's sub styles. Sometimes I can touch jazz (mostly big band with energetic drums and trumpets), classical (from piano to orquestras) and even lo-fi rap (a lot of lush and chill sounds, the SHP are dry but I got used to it, just increasing the low end a tad bit with EQ is acceptable for me, so I think I don't need too much bass), I also listen to some acoustics like Eric Clapton, Neil Young etc.
I have to decide which of these genres I prefer so I can choose a headphone that benefits them. But I listen mostly to the rock, big band and lo-fi rap songs.
I'm leaning towards the Hifiman He4xx, but some songs like Jesus Etc. from Wilco and Harvest Moon from Neil Young must sound so amazingly beautiful on the HD650
(If you have one pair laying around, I'd love if you tested it with these songs and gave an impression), it's an experience I plan to have someday as well.
If you have other suggestion under 200 or close to it I'm open I think (I'd prefer a open set of cans). What put me in this confusion were some quotes like: the Hifiman has is great with all detail but the HD650 has more musicality, more pleasure while listening.