Volunteer shift signups are working again

I've made some changes to how we do Angular now that I have an extra year of Angular experience and have a better idea of how to write idiomatic and testable Angular code.  (Still no Angular unit tests for the signups code, but at least we could easily write some now, whereas before it was out of the question.)

I'll leave a bunch of inline comments explaining what I did.
Unrelated minor fix.