I have heard of putting velco strips before the holes/slots in the trampoline catch the sheets, but never tried it.
To help clean up the tramp, the crew can hold the jib sheet in one hand, and the traveler sheet in the other hand, and coil up the balance of the mainsheet and put it on her thigh, but allowing enough slack in the sheet for the skipper to work the main. With the crew holding the jib sheet in one hand and the traveler line in the other, it helps stabilize the crew out on the wire by creating a triangle preventing the crew's upper body from swinging fore and aft, and pulling on both sheets simultaneously adds feet to deck pressure.