1st off the front tongue jack offers very little in stability. That coupled with the sidewall flex on the tires makes most TTs wobbly. A simple cheap solution is to get a couple Vise grip C clamps and clamp a piece of anything solid like a 2x4 or a piece of angle iron diagonally across the front and then the rear jack.
Clamp it to one of the bases and then to the frame up on the opposite side. Do one for the front and one for the rear. This will take the side to side movement out. Then for the front to back use some good chocks.
If the diagonal braces work then invest in a JT Strongarm type setup.
If you're still getting some bounce then a couple extra scissor jacks near the tires will take care of that.
