You are writing:
I'm not willing to minimize the scope of the question(s) from medicine
to organic microbiology. The point of these questions is to provide a
recovering civilization with an early stage jumpstart. Once they get
to where they can only make progress with interdisciplinary research,
that's out of scope.
This gives me a feeling that your idea of jumpstarting a civilisation is limited to technology and natural sciences such as biology, chemistry, and physics.
What about art, history, literature, philosophy, sociology, psychology? None of these can possibly fit in just three books no matter how good or thick they are. Choosing any three will be a matter of pure preference and nothing else. There are no objective criteria whatsoever to justify any choice (and I am willing to prove that).
Moreover, when it comes to art and humanities reference books will be useless. Practical guides can be of limited use in art techniques and applied psychology. However, without an understanding of the underlying psychological theory, any therapy can be also very dangerous and do more harm than good.
Of course, technically inclined people may say that humanities are less important and that we can create new art, literature, philosophy, and history once the world is rebuilt. This is true. But knowing the past can help to avoid another collapse as history tends to repeat itself just on a grander scale.
Psychology and sociology can be highly instrumental when it comes to rebuilding. Both sciences provide tools to improve productivity, avoid work-related injuries, raise morale, and most importantly keep the survivors' colony from collapsing. I would argue that qualified psychologists can do for rebuilding no less or maybe even more for your civilisation jumpstarting effort than qualified engineers. But I am biased here.
If you really want to collect a decent civilisation jumpstarting library you will have to pick narrower categories. And as you move toward humanities you might have to decide to abandon the three books approach and save as much as possible.
It also would be wise to create a list of references to good books on different subjects. Something like 'If you find these books keep them. We could not make a copy and store it here but these books are of great value.'
One more useful thing that you could do is to create a catalogue of big libraries around the world that contain collapse-prone books. That would be immensely helpful.