Do LT tires come in sizes an load ranges like I would need without doing modifications - 205/75R15 ?
We have no idea how much wheel well clearance or how much distance your trailer has between the tires or if your trailer needs a C or D load range tire.
Anyways....these are some 15" LT that other RV folks use with great sucess
Goodyear Wrangler HT in a LT235/75-15 C (50 psi) at 1980 lb capacity. Most LT tire makers carry this size.
And a Wrangler HT in a LT215/75-15 D (65 psi) at 2090 lbs capacity.
Maxxis LT U-168 are a commercial grade tire with several 15" sizes and have became popular with all types of trailer owners.
I see the Yokohama RY215 in a 700R 15 D at 2040 lbs capacity is popular on some of the other RV websites.
Do your home work on the numbers for your particular trailer needs.