A few years ago many TT's came without the Mor/ryde system for TT handling and towing. Most today have some sort of this system.
One our first 35' I added this system and was rewarded with the better handling but notice the same complaints you have. To correct this I added a scissor jack on each side as close to the tires as I could. This has helped a lot.
On our 40' TT I have done the same thing and am quite happy with the results. We normally don't employ the center jacks for an over nighter but for the long term they are wonderful.
Hope this help. I have no less than 8 years on this concept and am happy.