Well, although my knowledge of the internals is quite limited, it looks to me like there is precedent for this, involving page headers. As you say, a score can be placed multiple times. And each time it is placed, it can be interrupted at different points by page headers. I could see this being quite tricky -- but there is apparently a mechanism that lets it happen.
At the moment when Lilypond stops placing systems on the page in order to insert one of those page headers, could it not be given access to the information "this is partway through a score, and here is the title from the header block of that score"?
(If the answer is "no, it can't do that and it never will be able to," then that's the answer. I'm not trying to argue with you, just clarifying what I was imagining.)