Want my OPPO UDP-205 to sound as good as my Sony SCD-777ES

It would be pretty difficult to do that and get it RIGHT.
What is it about the Oppo sound difference that you want to change?
Are using the "audio outputs"? Or as a transport to a separate DAC?
If using the "audio outputs" line outs;
You could look into Swapping the audio output coupling caps to Mundorf EVO aluminum/oil caps.
I wouldn't change anything on the Oppo.
Wait to see if others reply; who know WAY more than me about good mods.

"Sony players that still sound great are starting to fail." The thing that is going to fail is the LASER and possibly the sled/drive mechanism. I'd contact Sony to see if these parts are available and buy two or three of them (each should be good for about ten years). BTW I'm a proud Oppo 205 owner and have no problem with the way it sounds.

I’d be surprised if Sony stocks the laser you need. When my Sony SCD-777 failed, I bought a replacement on eBay and had a friend install it. No problem! Be prepared, as some lasers are hard to find and expensive. My Oppo 105D sounds as good to me as the Sony.