help a Die hard ANALOG guy choose a budget CDP

Hi Jfn04,
Recently I was in your situation with a CD player . I had a Marantz SA11S1 player that was a wonderful sounding player. It had an on-board computer that crashed and could not be fixed. I loved the sound of that player and decided that I was going to stick with the Marantz brand.
  When the SA-8005 came out I bought one and after break in , I do not feel that I am missing anything musically with this player. It has that great Marantz sound and is well built.
if you check around you can probably pick up a new one for a great price.
highly recommended.
Carter

@violin  AMEN!  I am enjoying the 30th Anniversary SACD of Goodbye Yellow Brick Road on my SA-8005.  Rediscovering Elton.

If your Sony has a digital out, I would choose a HQ DAC like Schiit.
The Sony will spin the CD’s and the DAC will be updated for a much better sound. I tried SACD, was not impressed and not too many discs. Also I have used Spotify and Tidal. You can get very good sound from both with a good DAC running.

If I were to buy a CD/SACD player the Sony SCD-XA5400ES would be at the near top of my list.

I have run a Rega Apollo into a Schiit Bifrost Uber for improved sound.
I also run a Sony ES cd player into a Benchmark DAC1 for improved sound.

Just an idea....

I would get a good DAC and then an inexpensive transport. You can use the DAC with streamers and other digital sources going forward.
OTOH, the Oppo 105 is a pretty good DAC and is in your budget and can perhaps be used as a streamer (I own one but haven’t tried it for that).
I don’t know if the Oppo fills your ’analog’ criteria. The are no pops and clicks, speed stability issues, or dust bunnies hitching a ride on a stylus. Nor are there warped lps that gave been sitting in a basement molding away for the last 40 years that will play on it. You do get a significant amount of detail without an overly clinical x Ray feel.

Interesting question, in part due to the claim about how good the PS1 is.  I own two of the recommended PS1s, picked up for $5 each from a consignment store.  I find them to be terribly inaccurate CD players, with a bloated midrange, rolled off highs, and poorly defined lows.   Very easy to pick out in a blind comparison, due to how much they alter the sound as compared to a high quality CD player or DAC.   When I played my favorite demo cuts through a PS1 into a high end system, I was shocked by how much they were altered. 

A good CD player, and several have been mentioned above, will be far more accurate and defined, capable of producing a beautifully deep, nuanced soundstage.