after looking at the machine i can see what you want to do,first thing you need to do is find out the frequency of the game board output(its either 15k or 25k)-once you have established whether its 15k(cga) or 25k(ega) then you can contact companies to see if they have what you require,i have just spent 10mins looking and what i have found so far is that tft screens run at 60hz so they require a particular convertor;try these sites
www.converters.tv.comwww.highway.net.auwww.8liners.comif you can't find the frequency info of your game board let me know and i can contact sega for you,otherwise you can email gaminibandara@sega.co.uk for the information
i guess each converter will be about 100 u.s dollars and you will need one for each screen you fit.
there is a company that make upgrade kits for royal ascot to tft so the job can certainly be done-also i have seen a multi sync tft on the market,that would not require a converter
if i can help any further then please let me know