If you cut a strip of door skin to a width and length you find aesthetically
pleasing. for placing over the difficult seams it what ever position you
find works best.... you coat the doors shin on all sides with clear west
epoxy... spend a little time getting the edges sanded and use a small brush
to make sure the epoxy gets in to the end grain... when that looks like
something you can look at and live with... mix a batch of west thickened
with cotton fibers to the appearance of cool peanut butter.. make sure that
you have roughed up the place you intend to put the door skin brace with 100
grit sand paper.. after you slather the thicken west on the back of the
brace and on the surface you want to  support... mush it into place and
scrape away any excess... if it looks like it might slip or slide hold it in
place with masking tape or what ever measures are necessary... just get it
to stay where you want it for a few hours however you can work that out...
west is gap filling it does not need to be clamped to be very strong.. If
you use screws to hold the brace in place put a little Vaseline or some such
on the threads so they can be easily removed ... after all is dry you remove
the screws and fill the holes with a little more west and the holes
disappear from sight... of the surface is  properly prepared once the
thickened epoxy is dry it is not going anywhere..  an eight of an inch epoxy
coated door skin brace is very strong ... it can be  painted or varnished...
I would varnish it and it will be a nice aesthetic appointment..

I do not know if the application is right for this treatment but from the
sounds of it ... it will  probably work