I'm a CX owner and I love it, but I get why OP wants to avoid it — I have certain product types that I'm probably going to permanently have a lifetime aversion to due to negative experiences too.
That said, generally speaking, I think 2021 or 2022 will still be kinda less-than-ideal years in terms of getting a TV at a more reasonable price and with no burn-in risk like OLED. LG has been pretty damn aggressive compared to the competition in trying to incorporate new features and I think it's currently paying off for them big-time. After CES, there's a lot of good stuff still coming but not sure it's down to the pricepoints where it can be mass-adopted, and I think it will still remain an early adopter phase both in terms of feature sets and pricepoints for another year or two.
I'm optimistic 2022 turns things around. 2021 still has some good stuff if you're willing to compromise here and there on features and interconnectivity with other devices, particularly with HDMI 2.1 spec, but I don't think you get an affordable, no-compromises, non-OLED until 2022 or 2023... And I think that will only happen if OLED sales start to bottom out and demand for non-OLED stuff becomes more vocal, because despite concerns I think most people are willing to look past the burn-in risk and just buy up in mass quantities and it's creating a sense of urgent demand for the manufacturers to start leaning that direction with their panel selection.