Well, wouldn't you know it!
Right after I finished fixing the alternator my AC on the Civic decides to quit on me. I immediately thought it might have had a leak so i got a set of AC gauges to check the pressure and it turned out to be fine. Next I checked the pressure switch on the drier by jumping the leads and it failed to kick on the AC compressor. I also verified across the switch terminals that it had continuity, and it did. I tried jumping the clutch on the compressor and that worked too so I was stumped. Well, when I went to book an appointment with the Honda dealer and described what I did, the service manager immediately said "yeah, it's probably the thermal protector". I think this is one I'm just going to let them repair, but I'll post back on what the fix finally was when it gets solved.