I know nothing about Tic-80 export options, sorry. Only Pico-8!
My question was more about how to put the PICO-8 version as a playable file without overwriting the TIC-80 version which is already playable there (since itch only lets you put one playable html per page). I made some research but couldn't find anything, so I think that I'll have to leave the original version as the only one playable on the page for now.