: I want to be able to pick it up by the coaming with impunity.

I apologize but "impunity" is a very big word... I'm assuming you want a rock solid attachment. In which case, sewing the skin directly to the coaming is as rock solid as it gets. It may not seem that way, but it is the strongest way of doing it.
Another option for you might be to coat the skin with poly and then cut the hole and screw it together or open the seam enough to sew it on now, then coat it, then attach the rest of the coaming. This is assuming the screws are going through the base plate and into the coaming.
good luck,
Scott