I do Ophir and Alpine loop every summer (my dad was born in Ophir). You will do just fine with a 285 spare. Only two places to stay away from without a substantial lift: Black Bear and Poughkeepsie (the local rentals prohibit you from those two). I would also suggest you stay off the lower end of Engineer pass (Mineral Creek), were it meets US 550, with out at least a two inch lift. Thus to get to Animas Fork from the west side, go over Corkscrew, Hurricane, and California.
Check in with with the visitors centers in Ouray or Silverton for current local conditions and a free map.
The scenery is spectacular in that area. Enjoy!
Yeah, Corkscrew--Hurricane-California is my favorite offroad route along with the White Rim Road.
Some of the comments surprise me because I would put it the other way round: for Black Bear, you need wheel travel above all, not extra ground clearance. Some folks drive Mineral Creek (and Black Bear) in Foresters or XVs (downhill only).
I just use a 265 70 SL Wildpeak as a spare. It has served as a skid plate multiple times, including on Black Bear, with no issues at all.
In CO, I would just stick to 265 70 17 to minimize on road impact of larger tires. It is not like a 33" will really make any difference on trail, but it will be felt on the road which is 90% of the time even for those of us who offroad a lot.
Or, I would go 34" and up with re-gear so as to know I really have more clearance.
But that's me. Different people like different things. Except for front wheel travel. It matters a lot and lifts above 2" only rob from capability, don't add to it. I am on like 1.25" and with stiff suspension, it is plenty. With a soft suspension, it would hit a lot.
EDIT: to be more specific, the rolled Toyota videos and pics I have seen on Black Bear come down to wrong line plus lack of front wheel travel, particularly on one spot before the rocky switchback. I have also seen Jeep pictures roll at the start of the switchback were they hug the wall too closely on the right (easier mistake to make than one may think). So if the OP is headed there, don't do Black Bear without prior offroad experience and understanding of how to handle off-camber spots.