Lots of good ideas here.
The answer really depends on why your horse is scrambling, since we all know horses like to be unique and invent their own personal reasons for things.
Will start by assuming that the person driving is turning corners in a safe manner that should not be causing the horse to have issues. (If that is not the case then start there.)
Some horses do better when they stand in a stall that keeps them tight and sort of held in place. A spacious straight stall gives them nothing to lean on and they scramble.
Other horses are the opposite. A center divider that goes all the way down and a tight space has them scrambling to find a way to balance since they like to spread their legs out.
Some like the slant load, some like the box stall, etc.
Do you have access to other trailers, with different set-ups to see if your horse rides better in one set-up versus another?