After a childhood like that (the 'controlling, strict home' makes me think that Prudie's suggestion, a lock on the door, might not have been allowed) it doesn't sound that unreasonable that she'd want a space that was just hers.

Why not suggest a compromise: she gets her own room in your home - a private office, library, or whatnot - to which she can retreat whenever she feels the desire. You won't go there unless you're invited. However, in return, there won't be a bed in that room; she'll spend her sleeping hours in the bedroom that belongs to both of you.

It might be that what really matters to her is knowing that you do respect her privacy and space, and finally getting the chance to experience that kind of respect.

This idea should be a way to give her that without denying you the nighttime closeness that you want.