We'll probably have much better gene editing in 240 years time using nanotech with better targetting that required less or no error correction on the part of thd cell. Perhaps the Hyach kept a few "trophies" that still have enough intact DNA fragments that a whole genome could be reconstructed. Of course, as you state, if they erased every last trace of the Hyach-do, they've probably stuffed themselves.We can edit DNA now but we can't do it all that well. And without the Hyach-do around it'll be very difficult for them to isolate which genes are missing, especially since it's probably a host of genes.
Maybe computer simulation could work out the likely configuration of missing proteins and DNA sequences based on other lifeforms from the Hyach homeworld.
Actually, why am I playing "Let's save the Hyach"? Screw 'em. I never took the Hippocratic oath.