Maybe borrow someone else's HRM? Maybe even wear both at once, and see if they correspond? And maybe get to the doctor before October. I'd say (well, depending on what the doctor says), really hammer one ride (you said you weren't particularly tired on your 21-miler, and that you consider yourself slow). 162 doesn't sound like an exceptionally high max, so maybe you haven't found your true max, and are really really well trained at slower speeds.

Just a couple of thoughts - good luck!