In the past, I purchased fram mounted hitches for two passenger cars from U-Haul. They were very competitive in price and quality, are everywhere, were easy to deal with. The hitches were class I for several compact sedans, but they were well matched to the vehicle, were installed by them cheaply and without problems (Holes lined up, etc.). I wired it myself and could have installed it myself, but their installation was so cheap it wasn't worth my time or effort. U-Haul may be worth looking into and you would not pay for shipping of a very heavy object. I don't know who makes the hitches for them but since they have their name on it, it should be good.
J.C. Whitney is another possibility.
It sounds like a class III would more than meet your needs. A Class IV may be overkill, would add unnecessary weight to the truck and put a larger dent in your wallet.