Quote: "the door also vanishes completely quite often, I can only think that is an occlusion issue (It is. A quick test verified it)"
I experienced this problem in a mine gate, I remember that I solved collapsing all parts, except the animated ones.
Sometimes just setting "IsInmobile=yes" , I've got fix some other.
All those happens to me when animation complete (door close)>door vanishing>sometimes reappears when I go closest, or change camera angle of view, still the door have collision, and sometimes even open and close while remain invisible, I notice it because the sounds.
I must add I'm talking about an animated doors with various pieces, even doorway, plus the animated ones (the real door).
3com
Laptop: Lenovo - Intel(R) Celeron(R) CPU 1005M @ 1.90GHz
OS: Windows 10 (64) - Ram: 4 gb - Hd: 283 gb - Video card: Intel(R) HD Graphics