I got shown how to butterfly a haunch down to a thin 1” thick , spices, salt olive oil n show it over a bbq last season and its all I do with haunches now I've done a few mostly muntjac odd roe and a yearling fallow, by far the best was the muntjac, don't know whether it was because it was slightly thinner layered back or the applewood used on the small wood bbq and not gas
But muntjac over applewood i dont think you will beat with any species, try a muntjac first VSS its a head turner