Switching tire type/size is technically OK as long as the new tires have a load capacity equal to or higher than the tires originally supplied on TT.
ST > LT usually requires an increase in both size and Load Range.
Using higher Load Range tires also means you need to ensure you always are running the higher inflation
On TT tires should be inflated to the pressure (max) on the tire sidewall no matter if ST or LT
I suggest you bite the bullet and get 16" wheels as that will give you a much larger selection of tires, in Brand, size and LR