Thanks for the suggestion of Titebond III - since I have to buy something, I'll use that for putting everything together - might use PL200 for the foam though. The silicon will be to seal the edges of the door - basically gluing the outside trim to the door to prevent water from getting in, to help prevent rotting wood again.
A little update on my project - I've been able to save the aluminum trim, the outside ply of the plywood, which has the fiberglass on it, and the inside vinyl (although trying to figure out what to do with ripped corner - might just live with it). Everything in core will be new. Two updates I'm thinking about - but haven't decided on yet:
1) using solid blue styrofoam instead of the white bead stuff - not sure if this is adding more weight though?
2) Putting and extra stile down the center of the door for three total (one on the side edges, and one down the middle). Again though, wondering if I'm adding too much extra weight, and whether the pistons will be able to hold it up.
Any thoughts on the new ideas / weight are appreciated.