Wow, sounds like they sold you way under weight tires.
It's an option, advantage is the taller tire, clearance available that is, turns fewer times per mile than the smaller one. In other words, it's turning slower, which lessens the forces greatly. 16" tires are becoming very common in the trailer world too so that gives you choices.
However, I'd stick with an ST tire. Tandem axle trailers impart serious side forces with regard to side load going down the road and when backing up, turning tightly, etc. The sidewalls and tread area are designed differently to be able to withstand those forces better.
Am I saying that the LTs would be a bad choice? Not at all. Am I saying STs would be better? Yes.
But I'm still concerned about why you have popped three tires in 2000 miles. I'm sure you're keeping the pressure up to snuff, but you might need to check your gauge. Tires, even China bombs, blow out for a reason. First is low air pressure second is overloading, both overwork the sidewall and cause it to overheat.
There's always the chance you picked up something like a nail, but three?
Now-2014 Sierra 346RETS 5er BUB
Then-2002 Keystone Springdale 286RLDS TT
Nights camped in 2014-28, 2015-127, 2016-10