My bike has 3 chain rings and I never use the largest one; I'm almost always on the middle one. Occasionally I'll use the smallest one when going up a hill but it's fairly flat here.

For the sake of understanding how this all works I was wondering if I could remove the largest chain ring. It seems to me that the main issue is how to fix the shifter so that it only uses 2 chain rings. Would I just fiddle with the limit screws and end up with extra (unused) click stops on the shifter? Or do I need to get a different shifter?

Sure, just screw in the H limit screw.. you could substitute the outer chainring for a tooth less disc, keep your trousers cleaner that way.. and if you like that combo, a slightly longer right end of the BB re centers the chainrings into the space between them, which is how a double lines up.

you will most likely need a new set of shorter chainring bolts. also crank/spindleare designed to work together. if you take the outer ring off the chainline of the remaining two will be the same. chainging your spindle length to realign them for some reason may cause problems.

BTW a toothless ring or guard is a great idea.