I agree with Mike's opinion on an adapter added to the trailer pin box on these heavy fivers. I know a lot of racing and horse folks use the gooseneck, but the trailers are designed from the start with it. Not a bolt on. A lot of folks are adding them to smaller and lighter RVs. Your 32TK3 is not a real light wt. Call Lippert and ask them. They make the frames and can advise best.
Try asking your question here:
http://www.rvnetwork.com/index.php?showforum=32
These guys are on the cutting edge of design and have loads of experience on all things towed.
Bill