I can't give you any information about this outfitter, but I might be able to give you an idea about what to expect in terms of the turkey hunting in the Gila NF. I will preface these comments by stating that, although I live fairly close to that area, it has been many years since I have personally hunted it. I do know some folks that hunt it regularly, however, and these are my thoughts based on my history and their more recent experiences.
First off, although there are pockets of country that hold good numbers of birds, generally speaking, the density of wild turkeys in the Gila is pretty low and they can be widely scattered. I also think that, with the increasing popularity of turkey hunting, those areas that hold good numbers of birds are probably getting hit pretty hard, even in the most remote areas of the wilderness. Furthermore, a major fire a few years back burned a good portion of the wilderness areas and that has no doubt negatively impacted turkey numbers in those areas.
So, I suppose my comment to you would be that, if you are heading into this deal thinking that you are going to be put in the middle of country that is covered with turkeys and without any competition, I would be very surprised if that turned out to be the case. On the other hand, if you are looking at it from the standpoint of it being a horseback, wilderness-camping adventure and with the turkey hunting as being secondary to that, this might just be what you are looking for.
Then again, you never know. You might have the wilderness turkey-hunting adventure of a lifetime!