P-65 owner here. I'm in the same boat as you as far as the quality of cable tv and coming from plasma. Cable looks worse than it did on the plasma. Plasma was about as old as yours before it got that vertical black bar issue.
Colors in most cable programming appear flat and washed out. Especially skin tones - which also stray to a yellowish tint on many channels. HBO, Showtime and Starz programming looked amazing on the plasma. Especially the individual network series like True Detective, Ray Donovan and Black Sails. Now, I use the apps for HBO and Showtime on my Roku box because of the noticeable boost in quality.
I have the same blu ray player as you do - are you my doppleganger??? - and I havent played any 4k discs on it yet, but I did test the built in Netflix and youtube apps without any problems with 4k/HDR content. Maybe drop a line in the X700 forum? https://www.avsforum.com/forum/149-blu-ray-players/2951726-official-sony-ubp-x700-owners-thread-no-price-talk.html
I'm curious have you tried the normal picture type? I know a common view of calibrated settings are they are warm and yellow
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