Dave - I wondered how the FF/CMC build manual matched up to a Kitman build. Be sure to make notes in the build manual for others who might be so adventurous.
On my CMC with factory mounted doors, the lower rear sticks out about 1/4" on both sides. The door is made much like a modern car door in 2 pieces that are bonded together. 1 piece is the outer door skin and other the structural piece. Mine is black gel coat - when/if I paint it I will grind out the Bondo (pink) that CMC used to attached the 2 pieces together - that way I can close where it sticks out. I'm sure the bonding is the issue on yours.
550 2 door pieces as example - couldn't find image at RustyTubs for 356.
My hinges were a pain to mount. Once they opened and closed ok (done before pan was mounted). The hinges hit the shroud and I had to flip the hinges side to side so they were set wider. I didn't have issues with the rain shield using a later dog house OEM cooler. Maybe look for a shorter PUMA shroud or Thing one?