I was able to simply 'disable' play services (and many related services), mostly without issue. The only persistent issue I haven't been able to resolve is a constant notification from the wi-fi-manager service that pops up every time my connection changes, but I'm going to fire up adb at some point to see if there's anything I can do about it.

F-Droid is fairly complete, but you will have to figuratively glue some pieces together: DAVx, the simple suite of tools, and syncthing, in my case. A lot of smaller OEM apps (like, even the clock) will complain without gapps.

For maps I use osmand and the google maps PWA for POI search.