Inverts don’t need TTM. They just need to be kept in a fallow aquarium for 76 days.
Also TTM wouldn’t work as the inverts host a different stage of the parasite that releases free swimmers. So you would be transferring the encysted tomont with the invert during each transfer with the invert. Hence the reason you can just leave them in a fishless QT for the length of time that allows the free swimmers to release and die off.