Do this.
Next time you have the TT setup go over to a rear corner and push sideways on it. You'll be able to make the TT wiggle. If you look at the TT tires you can see them flexing as the TT moves back n forth. What you have is a pivot point at the tires. The tongue jack won't do much for lateral movement.
JTs on the front will only help partially. BTDT.
You can experiment with a long piece of wood or metal. Clamp it to the frame and an opposing stab jack. You won't be able to move the TT laterally after doing that.