you can go with 285...just be aware that the tire manufacturers usually recommend an minimum of a 7.5" rim for that size tire..so yeah, balancing might be alittle harder. saying that, i've had 285/75R16 BFG AT on my stock rims for 12k miles now, and haven't had an issue with vibration at speeds, or hard balancing or anything.
shoot, there's been a couple people with balancing issues of those same tires in stock sizes (265/75)...
the whole, won't install thing is kinda irritating. they assume you don't know anything, or they will only follow the rules. but you leave and a jeep guy comes in, they'll install the same tires on a 6" wide rim no questions asked alotta times.