Funny thing here. We bought our TT new this past May and it came with LT235/75/15's that are AT's? From the vast majority of responses on this thread I shouldn't have these tires on my trailer because they don't even exist.
LT 235's are very common, even today, as many of those "older" trucks that came with 15" rims are still on the road today.
To the OP, if you want to keep your rims but ditch the tires, look for the size I stated above. You'll be able to find many of them, even in LT's.
And to answer the one question you've asked more than a few times that has yet to be answered, yes, I've got rather aggressive M&S tires on my TT. When the times comes to change them out I'll put another set on there, too.