... Mattresses are very uncooperative things.
Yes to that! I had to lie on mine, to hold it in place, whilst I wrestled with the ratchet on the tie-down, one-handedly !
It wasn't heavy enough that I worried too much about it hanging off the back of the trailer a bit. So, I didn't need the bigger hitch, which makes the whole arrangement very long, and even more difficult to get around cycle path barriers.
Rolling it up lengthwise, rather than widthwise, did keep the overall length down, at the cost of a greater struggle to "roll" it up.