Project abandoned. I loaded up the IRMP library and got somewhat better results as far as seeing a code. However the variable number of bursts, or no bursts, per keypress remains. I even saw a few codes presented for keys pressed randomly four or five times ago - like a code for 'h' repeated for 'space'. That's just too weird. I tried some fresh batteries just in case. No joy.
Oh, well. It was only like 50¢ at a yard sale.