> What the patent actually covers is governed by the claims at the very end of the patent, and most of the rest of the document is generally irrelevant, per my very limited understanding of how patents work.

Correct. Only the contents of the Claims system matters to what is actually patented. Also, claims are subtractive/intersection, like all bullets have an AND function applied. So if you have a widget and it matches claim 1-8 but does not match claim 9, it does not match. That is, unless you specifically call out your "unions" - this usually looks like "the method of claim 8, but abc", "the method of claim 8, but def". That's how you do "unions." Kinda.

This is a gross simplification.