Optimizing HT setup for Analog: Where to begin?

The problem most likely is you are using an AVR - at least that is my own experience. I spent good money going from a highly rated Denon AVR receiver to separate Mcintosh and Lexicon HT equipment, with various speaker changes, trying to get it. It was great for movies/surround sound, but neither ever sounded great in stereo, never had a great sound-stage. Switched it all out to stereo. If you need to keep the HT, I would suggest getting a high-quality integrated made for stereo with a HT by-pass, you will get the sound stage you are looking for in pure stereo. That is my costly experience. One cheaper suggestion, disconnect the center channel and hear/see what happens. 

Right. AVR is crap. All of them. That and the center channel speaker, plus whatever else you have in the middle, these are all death to imaging and stage depth. 

The good news is a good stereo integrated amp and two speakers is way better quality for way less money than three speakers. With only two you can afford some quality wire too. DIY wire is your second crappiest component. There just aren't any good DIY wires. Period! I have one right now someone sent me as proof I am wrong, that only proved how right I am.

Where you start almost doesn't even matter, but since the AVR is such a total piece of junk, that only serves as a reason to keep the center channel you don't need, I would start with a good integrated amp. If you can stretch to $3k the Raven Nighthawk is an outstanding amp good enough to serve you the rest of your life, or for sure be an anchor piece for a good ten years. What's your budget?

Get a dedicated 2 channel only integrated. You are wasting your time trying to make a HT amp sound good for 2 channel audio. They are purpose built multi channel devices and should remain in that realm.

Excellent! ...and here I thought this would be a difficult question to answer! HT bypass - I’ll read up on this. I didn’t know it was a thing.

fwiw, I do run the AVR in 2 channel mode on "pure bypass" which is a setting that removes the digital processing. Also, I when listing to vinyl I have it set at 2 channel only mode. Probably doesn’t make much of a difference though I’d guess based on the feedback so far.

I do also have a PSA sub to fill in the lower end.

Is the power amp or pre-amp the most important when talking about sound stage / depth? I have pre outs where I could send L/R to a more capable power amp if you think that would be a good option.

My main problem, is that I have to keep the 5.1 setup / avr. There really isn’t a way around this due to space considerations.  Also, as far as budget -- I'd like to stay just shy of diminishing returns in audio equipment.  I'd expect this to be around $1k, $1.5k, but i'm open to stretching.  My theory is to spend enough to remove all reasonable doubt :)