Based on my experiences with my Tundra, keep your towing weight to 7K or less and you will have a nice setup. I pulled our old 29' Sunline TT that was close to 8K and although the Tundra pulled it OK, you could tell that it was a strain at times....not a rig I'd want to take through the mountains.
If you really want a larger & heavier trailer, trade in the Tundra for a 3/4 ton truck and you'll have plenty of capacity for a lot of larger trailers and fifth wheel trailers.
But there are quite a few trailers out there that are around 28' and would weigh 7,500 lbs. or less if you don't go crazy with carrying too much extra stuff.
Be conservative with weight ratings and you will avoid being in the situation of finding out that you HAVE to get a different tow vehicle. It happens frequently.
As per my signature, towing around 6200-6500 lbs., the Tundra is great. My trailer is 26'9" and we've done quite a bit of towing. We're on a long trip now and leaving Lander, WY today to head over to Colter Bay in the Grand Tetons. From there, we're off to Yellowstone, and then Glacier NP and over to Little Big Horn, Devil's Tower and the Dakota Badlands. Based on the trip so far, the mountains aren't a problem...I just let the truck do the work and can maintain speeds of 50 mph or better.
For a 3 month stay, most folks want the space of a larger 28-32' trailer. DW and I do alright with our smaller trailer for two months or so. This coming winter, we've booked a month in Lake Placid, FL and will take another month gradually heading home via St. Augustine (FL), Jeckyll Island (GA), Savannah (GA) and then to Salisbury (MD) to visit my sister before heading back to OH.
But, everybody has to figure out what works for them.
Take your time and look at a lot of trailers. Aside from quality, examine them carefully for storage space for what you need for a 3 month stay. Consider whether an outdoor kitchen is something you want. I love ours...we set up the Weber grill next to the outside stove and cook a lot of meals outside. The auxillary bar fridge is really handy for water, pop, beer, wine, etc. and makes more room in the main fridge for food.
Also, look at the awning length that comes with different trailers. I've noticed that a lot of more inexpensive trailers come with awnings that are 2-4 feet shorter in length than what they could be. It's one of many areas where they can cut costs in less expensive trailers.
So..good luck in your search!