Is it safe and efficient to charge a Li-Ion cell from mixed alkaline cells?
The residual energy in the AA cells is not valuable, the fact that the cells are portable, safe and cheap is.

That means using them for battery charging, that could use wall power, which is a few orders of magnitude more powerful and several orders cheaper (than full price batteries at least), is a total inversion of values and waste of time.

I too had access to a stream of partially used discarded AAs, and was able to make a steady donation of them to a charity serving the visually impaired, for use in their handheld illuminated magnifiers. They were perfectly matched to this service, as premature exhaustion of the cell was of no consequence to the users, especially given that they were free. The key here was a reliable stream, which allowed the service to abstain from buying full price cells.

If you insist on trying to recover the energy (I'm trying to imagine a desert island or post-apocalyptic situation where you don't have mains power, but do have the theatre's discarded AAs), then a) mixing AAs of a different charge state will result in premature run-down of the string of cells and loss of efficiency rather than damage (as long as you remove flat cells promptly) b) inverting up from a single cell is the least efficient way to do it, better to use a higher voltage and c) 18650 can be charged by a low current without reduction in life, as long as you continue to observe the normal charging envelope.