I do like doing things "right", but there is also a time and place for the simplest solution. This might be one of those times.
I agree the preferred method would be to modify the trailer properly, with either a standard tongue extension or a swing-away extension. But that involves cutting, welding, buying of materials, and the careful planning involved in modifying a load-carrying structure like that. Plus you'll either need to have, rent, hire, or have a buddy with the proper equipment for the cutting and welding portion.
But if a hitch extension works, we're talking $40 and 20 minutes to extend the wiring harness, and you're ready to roll. It's kinda hard to argue with simplicity like that.