I think you answered yourself, LCD tvs are crap for classic consoles, you can improve the picture a bit with a scaler but the good ones are expensive and you still will get worse picture than with a CRT tv, even with the filters. Also I´m sure you still can find a decent CRT at a nice price.
I personally use a 22" Sony Trinitron CRT tv for classic consoles and a LCD for the actual systems.