I know exactly what you mean. Our 282 Hemi does the same thing.
The trailer is still supported on the springs and axles and you will always get bounce unless you take the weight off the tires.
Try a sturdy jack under the frame in the middle of the unit -- under the door area and directly opposite. X wheel chocks are good for front to back, but don't do anything for the up and down motion. Test out your supplemental jacks too, make sure they are evenly supporting the unit without one being "tighter" than the others. I think one of the problems with the electric stabilizing jacks is that you can't snug them up, they go till the motor stalls. Remember they are only stabilizing jacks, not support jacks. I would suggest getting some screw type automotive support stands and use those rather than the stabilizing jacks if it really bothers you, or you're planning to stay for an extended period of time and place them under the frame members. Since the underbelly is covered, you have to take care.
I would not support the slide separately since you can stress the slide support members, that isn't really the culprit.
good luck and let us know how you fare.
Mark, Vicki, & Scout THE dog
2015 Hemisphere 282RK
2010 F250 Super Duty
1992 Goldwing Aspencade