Use a thick line for the hiking straps. Instead of sewing anything to the tramp, punch holes and put grommets in to thread the line through, space them such that there's longer runs of line on top of the tramp than below. You can dead-end the line at the beams or with an appropriate knot in one of the holes (I would try the beams). Where the line above the tramp, thread it through some soft tubing or whatever if you need a cushion. Depending on the size of the grommets you could probably run straps/webbing instead of a line.

You'll need to put something under the tramp to back up whacking with a hammer to set the grommets, but that would probably be easier than trying to sew.