Is there an amp that does 2-channel and all this?

You might look at the Anthem MX700 receiver. It does not have a phono stage, but you could easily add one and be below your budget. Have not heard it, but the Anthem gear is generally believed to have much better 2 channel sound than the mass market brands. If you wanted to you could also add a better 2 channel amp just for the fronts using the pre-outs. If you do that, the MX500 may be a good option, assuming it has pre-outs.

Sorry, that should be MRX 700.

I agree with the NAD and Anthem options. I'll also add the Arcam AVR600 into the mix. It retails for a bit more than your budget, but I just saw that there is a factory B stock on A-gon for exactly $4K. The internal amps are the best of any A/V receiver of which I am aware. I came really close to buying one of these, but ultimately decided to get an Anthem processor and outboard amps (at a much higher price).

I don't believe the Arcam's room correction is as sophisticated as the Anthem and NAD's, but I think the amp section is superior. Google the reviews on this piece - you'll be pretty amazed. I believe it has a phono section.

Arcam Avr 600. (I'm a dealer) I'm sure others exist. 2 channel on the Arcam is awesome. It does have room correction also. Do some reading on them.

So far the only receiver I have found that has all this is the Outlaw RR2150. This receiver has been well praised.

If I were going to go the separates route, could someone recommend a single company that would achieve my goals via separates with one remote control - preferably a nice remote?