I made a post over on Horse Trailer World too but I think BHW gets a bit more traffic so asking here also.

We have a single jack 11 ft LQ and the trailer moves alot when unhooked. This becomes an issue at night when one of us can't sleep and is tossing and turning, waking other person up. Has anyone used stabilizers for this issue? Found these on Amazon and wondering if these would work...just for the extra support. 

https://www.amazon.com/Camco-Olympian-Aluminum-Stabilize-position/dp/B000760FWU/ref=sr_1_14?crid=29F2R520H8VY8&keywords=stabilizing%2Bjack&qid=1647287379&sprefix=%2Caps%2C43&sr=8-14&th=1

Also thinking about purchasing some of the "X-Chocks" to stabilize the tires so they dont roll any. We are using normal chocks currently. Any other ideas? 

I have found when you unhook a couple things will help with all the movement....1) make sure your trailer is level both front to back / side to side, 2) use wheel chocks (pick one rear trailer wheel and place one chock in front and one behind wheel). If you are not parked on a level spot there are some great leveling options at RV dealerships...these can be stacked and then you drive up on them with a trailer tire.  That should minimize the side to side issue....obviously if you are leveling one side you chock the other side.  Chocks will help with the front to back motion.  Other than that I suggest everyone roll over a bit more softly so as to not rock the boat.  The leveling blocks I use...Tri-Lynx 00015 Lynx Levelers and they have their own zippered case so easy storage.  I recently used them under my jack stand as I was parked on softer ground and didn't want to sink.  I was able to lay them out so that I had more surface space vs a small jack stand only and didn't sink.  I use Roblock wheel chocks heavy duty with handle they are not the cheaper plastic ones that break.

We have these that we put at the corners.  Work beautifully.