If you are loading that tracor onto a 7k rated trailer then you are overloading the trailer, and its axles, so no need to worry about the tires. If on a 10k rated trailer then you would be wise to use tires that are rated to carry at least 2500 lbs each to get the 10k rating and this is very possible with your LT tires. It all depends on the load rating. You can buy LT tires with a load range E that are more than adequate.
I use a 10k rated trailer, empty weight is 2500#, tandem 5200 lb dexter axles, and LR E tires (10 ply), for my CK30 without a backhoe and it is great. My tires are trailer tires and not LT tires but the key info is the load rating which is stamped on the sidewall.
Big difference between LR C tires and LR E even though both are LT.
No problem with using adequate LT tires instead of trailer specific tires. The RV world has blown that myth out of the water.