I had my door apart when I added a power lock. It wasn't as bad as yours (I store mine indoors), but water had definitely gotten in. I've seen quite a few Winnebagos like that. I assumed mine was from leaving the door open in the rain a time or two, but once I had it apart I realized that wasn't it.
First thing. Where was the water getting in? I did a blower test on my motorhome and found it. I highlighted the issue in the image below. The fiberglass door skin isn't sealed to the frame. I carefully caulked mine.
Second thing. What happens to the water when it gets in? There are some drains on the bottom of the frame. BUT, the wood and foam sit tight to the bottom of the frame. ANY water in there gets wicked up into the luaun. I cut the foam and inner panel a bit short, and used some spacers (foam? - I forget exactly) to create an open channel where water can flow to the drains and get out, without getting wicked back up into the wood.
Can't help with getting it apart more though. You're as far as I had to go.
(I think your paneling is the same as mine. I grabbed an extra sheet at Winnebago years ago. Was a 4x7 sheet. If it matches, you're welcome to a piece. I work in Milford, very close to you I assume?)