Call Matt at New Mexico River Adventures. He knows the UTB, and may have the resources to help you with your plan, if he is willing to undertake it.
White Water Rafting New Mexico | Santa Fe Rafting | Taos Rafting
Also since you are talking about hiking in there, be wary of poison ivy. It is all over in the Lower box, (Acres of it..!) and it is also up in the Red River canyon (upper box) and down in Pilar. It could really ruin your day if you're planning on lots of streamside work. also (sure you already know this ) but the Gorge is really rough, in between the sections with trails, and the walls are mostly cliffed out. any sort of rescue would be prolonged.
Not discounting your experience or ability level whatsoever, it sounds like a really cool project, and very relevant to us NM river folks. just maybe hard the specific way you are proposing. (to document the entire run top to bottom. not in a watercraft.) specific sections would be much easier to access as stated by Dana. Anything is possible tho.
One other suggestion to consider (maybe for the future) would be to try and convince some of the class V rafters who have done it (IF the water level is acceptable for rafting, which i dont think it is) to charter a trip with them. then you just have to carry the raft and all your gear down into the gorge, raft some sieved out class V, and get your footage.
Its rarely done in rafts because of the somewhat heinous logistics, and dangerous rapids, but that (more suffering, lol) makes it more of an adventure, right..?
Lower Taos box will be much more feasible to access by boat when youre done with the upper, but the water levels could drop any day now. LTB can be kayaked down to 3-400 cfs, with 1-3 portages depending on how one feels about manky rapids. also its 16 miles long so please dont try to hike down that. its so much nicer to float...lol
Hope that Helps & good luck!