Same, if we are to put a false ceiling above the painting, wouldn't the gap be exposed?

Sure, but it's easy to just insert a box to cover the gap.
Or you can have a look at this post . Half way down, starting with: And – while I'm at it: you will find a fix to mask the more complex cut-outs, like from a spiral staircase.


Cec

EDIT: How hard can it be for me to get a link working today...