Thanks for posting your travel experience; especially your furnace problems. Hopefully the newbies will see the importance of doing a thorough PDI.
The bouncing can be an occasional 'harmonic' when the road, TT, and TV loads are just right... well, just wrong
If it is the TT only
and it is bouncing up and down but staying level and it happens rarely, there may be little that can be done. If it happens too often, then maybe adding shock absorbers to the TT would do the trick. IMO, it would be unlikely you have too little load on the front of the TT. If you haven't already, I'd try increasing the TT tire pressure to the maximum shown on the sidewall. This should change the tires natural 'frequency' and alter the bouncing rate.
If it is the TT and
your TT is rocking
(not staying level)
then it will take more investigation and probably changes to the TT and TV loading and the TV suspension.