Wow, that is one heck of a list of really nice gear. I think I may reach out to get your thoughts on how things compare and scale up. You obviously have some experience. Maybe you can share you thoughts on my below line of thinking.
I really wish there was a way sample them for a while. It may be a little crazy, but I think I am going to order a few options that are kind of considered the more affordable versions of some different styles headphone to see what I like, then consider moving from there.
First, I think I am going to order a set of the Sennheiser HD6XX. They are based on the HD6 series set that everyone loves but only cost $220. They are and open back dynamic driver with a well known sound. Their big brother, the HD800S seems to be well loved for a huge detailed soundstage, which seems like it would be great for identifying where all the sounds are coming from.
I also think I am going to buy a set of the HiFiMan Sundara which go for $350 which are and open back planar magnetic that seem to be well reviewed and recommended for an planar magnetitic in this price bracket. I guess that planer magnetics do really well at sound separation, so they could be good for what we listen to. Their big brother that seems to be well loved is the HiFiMan Arya or the Audeze LDC-X.
I also want to try a set of closed back to see if I like that sound better but I'm not sure what to go with here yet. I am kind of thinking of trying a Beyerdynamic set like the MMX300 or the DT770 maybe the 1990. I don't know as much about closed backed or where a good starting point would be.
After being able to really test out the three different sets, I would like to narrow in on what I like and I will sell the other two sets. I then think I will probably try a nicer "big brother" version of whatever I end up liking best to see if that is worth it over what I start with.
HD650 or 600 have nothing in common with HD800, completely different technology and sound signature. Almost opposite, one is lush, warm, with subdued details and good for open phones bass, quite slow for electronic and rock but great for jazz and classical.
The other is fast, hyper detailed, leaner on bass, very technical, microscope into sound.
I don't own HifiMan but had some Mad Dogs planar before, based on my experience with them and reading Sundara reviews, they are almost HD650 signature with lesser soundstage.
I would not recommend DT770 as closed phones, there are better options around.
Usually the closed are the trickiest one. After trying a bunch I've found Sony MDR-7520 almost ideal as studio phones. My second, reasonable for starters pick would be Sony MDR-1AM2, at least they don't do anything horribly wrong, super light on the head (feather like) and extremely easy to drive.
Forget BT phones, these are not good, Windows BT audio is pretty bad, plus there is latency.
As far as source goes, don't bother with fancy sound cards, had a bunch of them, on board audio is always susceptible to some computer noise. They are fine for gaming, but fall short for critical listening.
USB DACs with async receiver chips are very good these days. Look at those. I am using Auralic Vega/Taurus stack that replaced Chord DAC64, but it's probably out of your price range, the other one is Yulong Sabre DA8, it's less fancy but has somewhat decent (not great) headamp.
And once again, I highly recommend head-fi.org if you want to get serious about your music and need qualified advise.