You could just run a headphone extension cable from the back of the CX, set the CX sound output to Audio out (line out) or wired headphones and tv speaker for both to use. Then simply attach your headphones to the headphone extension jack when you need or leave it always in if you wish.
If you want to prevent that dreadful headphone hiss then look a few post above I linked a device that cost just over a tenner from rainforest which should stop the hiss.
But sure if you have high end headphones and just want the best possible audio quality, it wont beat a dedicated headphone amp with optical input although good ones cost around £100-170. I think most will be more then happy with the above headphone extension lead and that isolator device.
also I am not too picky on ppi on my 55CX the text is just fine for me so I wouldn't downgrade to 42inch again I had a 42inch before the CX so the 13inchs makes it that much better to game on and watch movies/stream IMO