Aha; you're right - the font does include the basic characters, and using it that way instead of building the string one code point at a time does indeed display the new emoji, like the transgender flag, correctly (and, of course, the accordion, also new in Unicode 13)
However, when displaying ordinary text, it's doing something weird with the space character, which is irksome - see attached screen.
So, I think in the interests of processing speed the best compromise will be to use the JoyPIxels font only when a message is flagged 'bigemoji' by the server, which means it has 10 or fewer characters, so spacing won't matter so much (and I expect most of those messages to be largely emoji anyway)