I don't know how gross those people must be, but my pads do just fine.

Gross as in gross weight?
HD600 pad wear isn't so much a lack of hygiene issue as it is a head size issue.  People with a large head will squish the pads to death.  People with a smaller head can get years of daily use from the pads.

If you do have a large head you can stretch the HD600/HD650 so it doesn't squeeze as much and squish the pads as much.  Extend the ear cups fully and flex (bend) the metal to stretch it out.  Don't try to stretch the plastic part of the headband, it may crack.

I get years of use from my HD580 and HD600 pads. Even back when they were my daily use headphones.

The sound quality of the Senns does depend on how unsquished the pads are.

I was gonna suggest HD600, Vali, and Modi. Haven't heard it myself, but from what Ive read i can't imagine it not being stellar for the money.

Hammy: you want a setup for acoustic, classical, and videogame music right? I'm listening to Bifrost Uber > Vali > HD 600 right now, and it all sounds good to my ears. Was just playing some tracks from "Greatest Video Game Music" and Oscar Peterson Trio's "We Get Requests"; there's a good sense of spatial cues, and tonal correctness.
Individually, the HD600 and Vali are also good investments. They scale well. I noticed the Vali sounding better off Bifrost than my Xonar soundcard, and there's no shortage of testimonies where the HD600 is concerned. Both are great choices.

The issue with head size isn't about how how far you need to extend the ear cups.  It's about head width.  If you have a wide head like a sumo wrestler you'll kill the ear pads.  If have a skinny head more like a pencil neck geek you'll get years and years and years of use from the ear pads.  I get years of use from the HD600 ear pads.

The HD600 will work very well from a little Schiit stack.  I have the little Modi DAC and Magni amp.  Does very well with the HD600.  Much better than you would expect from a $99 amp.  Surprisingly close to the original Asgard amp with the HD600.  I've not tried the Vali amp with the Senns, so can't comment on that.

The HD600 will do well for the music you mention.  Well suited for acoutical flavors of music, classical, jazz.  They'll train your ears for what is a neutral sound signature.  I also much prefer the HD600 to the K702.  The Senns have a certain soul to the music that the AKG seems to strip away.

Strato, are the HM5 velour pads relatively easy to install on the HD600? I might give that a shot for kicks, but I can't say I've toyed with them that much to know how easy or difficult it might be.