We have been down this road...one Class C, two gas Class A's and a 36' Beaver diesel pusher...obviously the Pusher was the most stable...
We have had a 36 foot 14000 GVW Big Horn now for 5 seasons...I have towed it for over 20000 miles...some of these were with a SRW F250 and F350 and now with a Chevy Dually...IMO...even the two SRW trucks were steadier on the highway...the dually is even more stable...
X 2 on trying all the trucks...that is a heavy fiver and the new Ram's are the King of Tow ratings...the GM's have a warranty
Regards