Our TT is about the same length. The stock stabilizers are okay for a weekend, but for longer periods I picked up a pair of scissor jacks at Harbor Freight, cheap, and placed them on wooden blocks under the frame just ahead of the forward axle. Setting all six "feet" on RR tie or larger blocks I think is key to stabilizing. They form a pretty solid foundation and don't require stretching the jacks very far.
Our good sized dogs can run around and jump on stuff, and 95% of the shaking is fixed, for about $40. I doubt if spending multiples of that would give results worth the price or the effort. For me, anyway.