That plastic tub cover snaps in place, WP had trouble with the plastic tabs breaking that hold it in place, when you raise the top of the washer if the plastic tabs are broken I may still have the kit to fix this problem.
It should not be necessary to secure the tub in this washer when you are on the road, If you want to put a piece of soft foam between the top of the tub cover and the underside of the top it might not hurt, just stay away from the lid switch etc as they are easy to break, This washer only needed its tub braced when it was being shipped on its side, back etc.
I would try to find a new timer, once these get messed up it can be hard to fix them. We used to see a lot of these get broken because of the way they stick out from the machine.
John L.