Tangentially, are there any good map websites out there that show me the elevation at a point I click on?

I've found a lot of providers lacking in this department, even if they clearly have height data for showing contours/3d views.

well, not a website, but https://wiki.openstreetmap.org/wiki/JOSM/Plugins/Elevation seems to do it

https://wiki.openstreetmap.org/wiki/Open-Elevation also seems easy to integrate