So I figured out a mediocre solution to my organization problem. Haven't tackled my mods/maps situation yet, but I have created an "engines" folder in the Quake directory to house my engine files. Initially I tried creating shortcuts to the respective engine exe's using the -basedir parameter, but SQLauncher wouldn't see it because shortcuts aren't technically exe's themselves. So I used symbolic links instead. This preserves the exe extension so SQLauncher will see it.
So now I simply have 3 symbolic links in my root directory for quakespasm, quakespasm_ad, and quakespasm_spike, with their files tucked away in an engine container folder. Adding more engines will be simple, tidy, and they should all cooperate with SQLauncher.