I also have a Claytor. I always have a spreader at the head end. I don't carry a bar with me but simply pick up a stick from the ground and break it to size. It doesn't have to be the exact length each time. I've done a lot of hanging this summer and have never been unable to find a suitable branch.
I also tried a 40" pad and it was way overkill. It also tends to bunch up. Through much experimentation I've conluded the 1/2" thick 24" waffle pad at Wally World with attached wings work the best. Why carry more when it's not really needed.
My pad can be seen here. http://good-times.webshots.com/album/560834203BtHMbJ There is a little note under each pic. The black strips are ripstop nylon and act as a simple hinge. I'm very happy with this sytem and the Claytor hammock in general.
Welcome to The Claytor Club!