Out of the headphones on your list, I think the Fidelio X2, SRH1840, K712, and HE-400i are the best ones in terms of overall sound quality. The Alpha Dog may be good also, but I haven't tried it so can't say. However, being a closed back headphone, I doubt that it can match the overall sound quality of the open backs on the list. Well, to be fair, I own the SRH1540 and NAD HP50 and both are seriously good sounding headphones, despite being closed back. However, I do think that they are lacking the spaciousness, effortlessness and overall realism of good open back headphones like the ones I mentioned previously.
I only tried the SRH1840 briefly at a local audio shop a few years ago, so I honestly can't remember much about how it sounds, but I remember being impressed with the accurate tonal balance, clarity, openness, treble resolution and overall realism of these headphones. The problem is that they don't measure well on paper - if you check out the graphs for them on Inenrfidelity, you will see that the SRH1840 has a lot of distortion in the bass and mids. Personally, I am not sure I found this to be an issue, but I do recall hearing the bass on the SRH1840 as being somewhat weak sounding and lacking extension, which may have to do with the high distortion. However, I do think that it is at least a reasonably technically capable headphone with a very pleasing tonal balance for most instrumental, jazz, vocals and any music that doesn't require a powerful and deep bass response. I can't say how SRH1840 fares in regards to speed and transient response though - it's probably good, but maybe not great. They are easy to drive headphones as well, so they will fit your need in this regard.
I really like the Fidelio X2 - I think it's a seamlessly balanced headphone with perfect transitions from bass through mids and treble. It is an exceptional all arounder that can deliver great sound on many different types of music. It's not strictly neutral, as it does have an emphasis on bass and lower midrange and a slightly laid back treble, but I find this balance to be very natural sounding. As the sound quality of the X2 is great at all frequencies, the extra bass emphasis sounds tight and pleasing without muddying up the higher frequencies. I wouldn't call the X2 an exceptionally fast headphone, but a really well controlled and balanced headphone. Whether or not it will suit your need for "fast" music may be just a matter of personal preferences. It is also easy to drive like SRH1840, so it will also suit you in that regard.
I haven't heard the HE-400i, but I have owned the HE-500 and based on measurements and other peoples' impressions of the sound of HE-400i, I can safely assume that its sound character and sound quality is somewhere pretty close to that of the HE-500. In that case, I think the HE-400i may suit you quite well, as it should be very fast, with excellent transient response, thanks to those planar drivers, yet also very well balanced tonally with great extension in the bass, as well as treble and great mids. Resolution and clarity should be excellent. The problem is that planars are usually quite hard to drive well, so the HE-400i is unlikely to sound anywhere near its full potential unamped out of a smartphone. In fact, if not proeprly amped, the planars can sound somewhat muddy, veiled and "slow".
I haven't tried K712 either, but based on my experience with K612 and Q701, I would say that the K712 will also need a pretty powerful amp to deliver its full sonic potential. A smartphone is unlikely to drive it sufficiently well. The headphones will sound flat and boring when underpowered. The sound quality is really good though - the higher end AKGs are really well balanced tonally, fast, resolving and very spacious sounding headphones. They are probably the most neutral on your list.
SRH1540 is an excellent closed back headphone that's easy to drive and very comfy. It sounds spacious for a closed back with good instrument separation and well extended, well resolved treble. It is generally very well balanced, except for the sub bass, which stick out like a sore thumb. The sub bass is really quite emphasized on the SRH1540 and with bass driven music this can lead to some noticeable disbalance with the bass intruding a bit into the lower mids and causing some congestion and loss of finesse.
NAD HP50 is balanced very much like the Phillips X2, but I do think that the NADs have somewhat tighter, better extended bass and a cleaner treble. The X2 however, sounds more open, spacious and dynamic. I think X2 is the better sounding headphone overall, but HP50 is a bit more tonally balance, more neutral and cleaner sounding. If I had to choose one, I would get the X2, Both are easy to drive, but do scale very nicely with better amps and DACs as well.
I haven't tried the other headphones on your list unfortunately, so can't say anything else about any of those. Based on what I wrote above, I can conclude that out of the headphones I've heard that are on your list, the Fidelio X2 is probably your best bet - it's really well balanced, quite resolving, open, spacious, natural sounding. It's just a great all arounder for a lot of music and is easy to drive, so it can reach much of its potential out of your phone, as long as your recordings and bitrate are sufficient. SRH1540 may be a good option as well, if you don't mind a strong kick in the sub bass. In some ways it sound cleaner and more neutral than the X2 I think, but not quite as well balanced as X2 overall. HP50 is very good and sounds somewhat like a cleaner, but less spacious X2....
I can also recommend trying out Audio Technica ATH-MSR7 - it's likely the cleanest, fastest and most resolving headphone I've heard apart from HD800. It's an easy to drive closed back headphone and doesn't sound particularly open and spacious, MSR7 also has some emphasis on the upper mids and treble, so some people may find it too bright and light in the bass, The bass on MSR7 is really tight, but does get overshadowed a bit by the stronger mids and highs. The treble can also get a little harsh and fatiguing at times. The headphones are quite forward sounding and not forgiving of poor quality recordings or low bitrate. MSR7 is certainly not for everyone, but it has transients/speed and resolution that is unparalleled in sub $1k headphones in my opinion, so if you are looking for a headphone that can handle the most complex music without any hint of smearing/grain and with crystal clarity and razor sharp definition, then the MSR7 may work very well for your need. You will likely want another headphone with a more balanced, less aggressive and more forgiving sound to pair with the MSR7 however, as MSR7 is really too forward and unforgiving to be a good all arounder IMO. You may be excited by the forward, aggressive and extremely detailed sound of the MSR7 at first, but it's bound to get fatiguing after a while. However, it's worth getting despite all the flaws because its a superb reference headphone for critical listening.
IMO, Fidelio X2 and MSR7 will go very well together. The former for relaxed listening at home and the latter for critical listening and portable use...
For portable use, you may want something with better isolation though. HP50 and SRH1540 offer superior isolation to MSR7... That's why I have several headphones - they all have different strengths and weaknesses and having more means that you can cover more of your needs... As people like to say around here, "Wecolme to head-fi and sorry about your wallet." lol Good luck with choosing the right headphones!
