How to glue hardwood to plywood core door?

I have seen 5/16 face nailed (brads) hardwood planking in old (100+ years) in Vancouver. The usual floor construction was 1x8 shiplap, run diagonally across the joists, then the hardwood (or sometimes edge grain doug fir) nailed to cross the joists at right angles.

Anyway: If you can get a supply of thinner cut hardwood, then I would consider making a door by gluing and screw two plywood panels 3/4" thick together, then surfacing each side with 1/4" thick hardwood strips. This would give you a 2" thick door, which I think is still a standard thickness that will work with conventional hardware. By having the same material on both faces, the stresses should balance -- assuming similar temperature and humidity on both sides.

I leave the problem of hiding the plywood edges as an exercise for the student.

Panel and frame doors appeared to address wood movement problems specifically, as well as planked doors. I don't think there's going to be a problem if you'd glue 1/8" thick veneer to mdfplywood substrate, since it's an interior door and there's enough of holding power in modern glues to withstand movements of thick veneers (if there are any). 1/8" is sufficient for sandingplaningscraping but not thick enough to cause shrinkage cracks.