I don't see the problem? Frame flex and bed movement under load is normal. The b&w Bitches are not attached to the bed in any way and the ball in its mount has less play than a regular hitch in a reciever. You might want to watch for cracks in the collar around the ball but if that movement makes you panic sell your truck and buy a microbus.
Personally I think a 5th wheel hitch pulles better than a gooseneck. Most gooseneck trailers are set up to have a kingpin that can be slid in place of the ball reciever. Just make sure the 5th whgrl hitch is rated according to your trailer. I had a bad case of a 16k reece sliding 5th wheel hitch sliding while in motion. But the hitch was way over loaded.