My trailer is a little shorter than yours, and I have the wiggle. I have all stab jacks down and X-Chocks snugly in place, and I can feel virtually every footstep from my bed. Before I got my X-Chocks, I could feel it in my bed whenever my brother rolled over in the bunk at the complete opposite end of the trailer. So the chocks DO help, but do not eliminate. I was also thinking of adding jacks on the frame by the axles, so it's good to hear from people who have done that.
2014 Jay Flight 28 BHBE
2015 RAM 2500 6.4L HEMI, Tradesman 4x4, 3.73
Blue Ox SwayPro (BXW 1503)
Upgraded from an REI internal frame backpack and a Eureka 1/2 dome tent!