You absolutely will not find a 2K tube amp with bass except some very shaky 6550 amps about 20 years old which are remotely close.
The one important qustion is your preferece in terms of volume, now be honest. If you are genuinely a quiet listener which all the "truest" audiophiles seem to claim. You can get SS controlled but not thumping bass out of a tube amp. Turn it up to real levels and you will get major, miserable bass distortion. No $2K tube amp can do otherwise that I know of. A hybrid amp doesn't sound like tube poweramps.
Sure biamp, but that is still a challange and easier said than done. Firstly there are only decent to good tube amps for $2k to start with, some no doubt (dep on vol see below),but then you want $4k bass Solid State sound for the bottom end, not cheap SS bass, from the little you have written.
I am not a 75db listener. Yes I just came out and said it. I have always seem to enjoy music with dynamic, about 90 db crescendos when I want to really get into it. That is if I don't feel too rambuctious, then of course it should go to 95 or even higher. At 80-85 I'm ok when using my tube integrated at its max before "tube blow" (=distortion) sets in, or my wife is around eitherwill causea sudden unwelcome loss of volume. I would prefer the option of going louder but that is what most $2k amps can do at best. If you have a wife- well uh, there is no stopping that volume control.
As for all you Nattering Naebobs of Negativism, the OSHA hearing loss data is based on a full day of exposure, I am lucky if I get a couple of hours of free time. I have read hearing loss is worse in in these kids with those blasted ear buds, than people my age, late 40s. I have some hearing loss in theory, in the high frequencies ranges as I age, which I imagine I am not magically immune to, and so should you, it's natural (nothing to be happy about but nothing to be ashamed of either). To those who claim they have no loss of high frequency hearing above the age of 40, because of their meticulously careful listening habits, I recommend you see a true audiologist then Psychiatrist to deal with the truth.
If you play really loud about 100dB if I recall, for hours on end you can of course hurt yourself.
If you really want chest thumping tuneful bass with holographic tube sound at real listening i.e. reasonably loud volumes in the 80s adjust your budget by triple. Sorry but big power tube amps or big sounding tube amps cost a lot. You don't need watts all the time but you need the big trannies to control bass, or some like the rather sterile IMHO sounding class D or ICE based amps. Or get a real sweet $2-3k amp like the Manley EL84 sterbloc and keep your BAT SS for the bottom and Biamp. Now you just need to figure out how to get them playing in synchrony. I guess TVAD can tell us.