1) I need fast, easy manual focus. Like an old Nikon SLR.
That one is going to be tough, unless you're willing to get a full frame body: crop bodies have smaller viewfinders than the film dslrs you're used to. Anything above a D80 (D90, D7000, D200, D300 for Nikons or x0D Canons and above to name a few) has a relatively big viewfinder and there are focussing screens specifically for MF operation (split screen, microprism screen, etc.). These focussing screens cost ~50, I think. Just forget about cheap dslrs (entry-level models), their viewfinders are tiny.
Full frame bodies such as Nikon's D700, D3 and D3x or Canon's 5D (Mark I or Mark II) and EOS-1Ds have much larger viewfinders. Of course, you should also invest in a focussing screen. I have a D80 and I find it next to impossible to manually focus with my 80-200 mm wide open. I don't have a focussing screen, though.
2) I need fast, easy (ie quick knob, not a menu) aperture/shutter priority or manual exposure setting. Like an old Nikon SLR.
All modern dslrs which are targeted at ambitious amateurs and above have that.
3) I need the picture to be taken ASAP after I press the shutter button. Some digital cameras have a big delay before and after pressing the shutter - far worse than a manual SLR. What is that about?!
Not a problem with the current crop of dslrs.
4) I like to take some action sports photos. Fast Ektachrome anyone? So, I want a fast digital sensor.
Pretty much modern dslr offers ISO 3200 and even higher ISO settings. The D7000 goes up to ISO 25,600 (try and find a film that's that fast
😉). Which setting is bearable in terms of quality is a matter of hot debate and personal preference.
But, I still like fast, easy GPS. Like an iPhone 😱
You can get a small GPS adapter for upscale Nikons, for instance, that records the location directly into the EXIF data. I have a GPS logger which I don't really use, because it's too much of a pain for me to combine the GPS data with the photos. I'm sure there are similar adapters for other manufacturers as well.
I can't afford Canon or Nikon's best full-size DSLR's right now-- but, do any of the listed compact/regular DSLR's above come close(r)?
That's hard to answer unless you tell us what standard you use to compare cameras. If you tell us your budget and your current equipment, we can give you more specific recommendations. If you happen to have old Nikon lenses, you could still use them on better Nikon bodies (D7000, D200 and up).