Just an update on this thread: installed a new door sensor/switch and everything is working just fine.
But, it's still very confusing. The old door sensor was a normally closed switch. I bought both normally open and a normally closed new ones. The steps worked correctly only with the normally closed switch; with the normally open, they worked backwards. So, it's not clear why the new switch worked, since the old one seemed to be perfectly functional, according to my ohm meter.
But, they're working, everything's cool. Thanks for your input!
