The one foot length and 1200 lb weight difference, shouldn't make that much difference to your TV. If majority of that extra weight, is up front, could be, you need more air pressure in TV tires.
Not enough tongue weight, low air pressure (sidewall flex) in TV tires, or, hitch height being too high, can cause those symptoms.
Too much cargo behind TT axles?
Tires properly inflated (both TT and TV) and balanced?
Hitch head too high?
Holding tank locations?
My tongue weight drops 200 lbs when I fill the fresh tank. It is located behind the axles. When traveling with full water, I try to load heavier up front.
I have an Andersen hitch. It does help with bouncing and sway (from bad roads), but, if you have a loading, tire, or hitch height issue, it won't make your problem go away.