Can I assign a keyboard shortcut for "Add Spacer Down"?

Noted. As it happens, I'm already working on it. No ETA though.

The still missing album feature might help in your case, once it got reimplemented

I only want to mention 2 methods that might help in your situation:
- You can save spacers with different lengths in your palette (draw them with Ctrl+Shift to the palette).
- You can apply a shortcut to "Apply current palette element" (I assigned Ctrl+<, which is very handy)
The combination of these 2 methods could speed up your work substantially.

Impressive work, good luck on getting that done, and hopefully published (?) !

As mentioned, we really do want to make it possible to add shortcuts for literally everything on the palette, even custom palette elements you add yourself. Meanwhile, though, I do have some other suggestions for you that may help:

1) I can't see any value in setting min system distance to 0. Are there really pieces where you want the bottom staff line of one system literally touching the top staff line of the next (or at least, as close as they can get without the clefs overlapping?) Assuming not, then 0 is way too low. Anything below 4sp should be completely out of the question, as you never want systems closer together than a staff height. And really, it should normally be at least as great as the grand staff distance (distance between the staves within a system), as normally you want more space between systems than within them. In the rare cases where you need to pull systems closer together than the min, you can use a "fixed" spacer. So if I were you, I'd do an experiment using a copy (!) of your score: try deleting all spacers (right click one, Select / All Similar Elements, Delete), then playing with those distance setting some more. Frankly, I'd suggest starting by going back to the defaults. Really, the whole point of the min/max settings is do do exactly what you are trying to do manually - make sure systems are spaced appropriately when there are different numbers of them per page. You shouldn't be needing to fight so hard to get the results you want. With good min/max settings, spacers would be needed only rarely.

2) Even if you can't get min/max to do exactly what you want right out of the box, you can probably still take advantage of them more by letting them work a little hard. I recommend letting max system be quite a lot bigger than it currently is - the default of 15 might be too big, but I'm guessing around12 will be nice. This will prevent you from needing to add so many spacers to increase distances, but it might result in a few pieces where there is more space than you want. Still, a clever way to decrease the distances on that page is to add a spacer below the last system. Increase its height to push against the bottom margin and the spaces of everything else will close up accordingly.

3) I like your idea of using AutoHotKey, but instead of using mouse movements, I recommend using the palette search, it's almost certainly both easier and more reliable. Ctrl+F9 is the shortcut for palette search, follow that by the name of the element you want to apply. You can even customize the names

4) Check out "Notation Express", developed by Philip Rothman of "Scoring Notes" (formerly "Sibelius Blog" fame. It's an extremely clever interface that you might find useful in itself, but it might also give you ideas for how to implement other useful hacks (he uses the palette search trick, I know). Here is the link: https://www.nycmusicservices.com/notation-express/

5) Kind of late now, but FWIW I probably would not have done these all as one score. The "album" feature would have allowed combing them into one later, but even failing that, assembling a book later using something like Adobe Acrobat, or free alternatives like PDFsam, is in some ways easier. In other ways, not so much, because if you want to change a style setting, you need to apply it to each song. But that process can, I suspect, be automated through command line scripts or plugins. It's also not quite as painful as you might imagine to manually load a new style file into 100 different scores (trust me, I just did this myself a few weeks ago for my own theory text - see https://musescore.com/user/2975/sets/5099981. Once you get the sequence of keystrokes to automate the process (Alt+O, Up, Up, Enter, etc.) I could do it in seconds, and of course, you could AutoHotKey that too. Something more to think about for the next project, though. By then, maybe we'll have an improved album feature back.

6) I see you have a custom palette going - good job there! I guess that's not a suggestion :-)