I tackled the door repair yesterday. Thankfully, the wood frame perimeter was only three sides, with the strike side being a full-length galvanized channel. This made it possible to insert the new frame without removing either fiberglass skin. The bottom strip, and part of the lower hinge side strip were pretty rotten.
I hope to keep this trailer for quite some time, so I didn't want to have to do this again. The wood strips were 1-3/8" thick, and ranged from 1-3/16" wide to 1-5/8" wide. I considered doing them in douglas fir because it is more rot resistant, and it is more stable dimensionally (less likely to bow, twist, etc.) I instead bought a 4x4x8 douglas fir post, and ripped it down to the dimensions I needed. Problem solved.
I'm happy with the results. I think this door should last quite a while.