Are there E-pianos with MIDI over USB
It would be difficult to find one without that these days. If a digital piano has a USB port (almost all current models), it has MIDI over USB. It used to be that they often required you to install custom drivers on your computer, drivers which would likely no longer work on any modern computer, but that probably hasn't been an issue for a good 15 years or so. (And anything that had that issue likely had 5-pin MIDI ports as well, so there would still be a way around it.)
Yes, 5-pin MIDI ports are still common today. Almost any digital piano over $1000 or so has them. and some lower priced models have them as well.
Are there stage pianos that don't cost an arm and a leg?
Sure. The hard part there may be drawing a line that everyone can agree on between what constitutes a stage piano. But the Kawai ES60 has 88 weighted keys and 1/4" outputs, it's under $500, Not that everyone would necessarily agree that a stage piano *must* have 88 keys, or a hammer action. (Or even 1/4" outputs for that matter, though while it is possible to use a keyboard without 1/4" outs *as* a stage piano--I've used the Korg Liano that way--that could be more a case of using something that isn't a stage piano as a stage piano.) And then some people might define a stage piano in part by what it
doesn't have, Some people might say a stage keyboard shouldn't have speakers, so then you might look at, say, a Korg D1 (undoubtedly a stage piano and still in the lower half of your budget), but in fact, in recent years, it has been more common for stage keyboards to sometimes include speakers as well.
Are there midi controllers that have good enough action to warrant always plugging it into a computer?
Sure. There are a good number of them that are as good as what you might find in a stage piano... sometimes even the same exact action is available in models with and without built-in sounds. If you want a controller with piano action that is above average and arguably even better than that of many stage pianos in your budget, you could look at the Kawai VPC1 and Studiologic SL88 Grand.
Back to the main topic...
Since your #1 criteria (based on the subject line at least) is best action, I agree with Biggles that Kawai ES920 and Yamaha P525 are worthy contenders, those are those brands' best actions in the under $2k price range. CK88 is a great keyboard, but not one with a first-rate action. I'm not sure how usable the Korg C1 is as a slab, but you can also get the action of the C1 in the less expensive D1, if you give up the "nice to have" internal speakers (I think the C1's piano sound is better than D1's as well). If you want to checkout Roland's best action, the FP-90X is just on the border of your budget.
re: "Really good piano samples, with velocity and such" - They will all respond well to velocity. Which ones are "really good" is somewhat subjective. But that list gives you a good selection of the better actions available, and all of them can also be used as MIDI controllers, so that when desired, you could also use them to play other/better piano sounds from your computer.
