Tested the JTAG circuit again with the first 74HC244. Confirmed: it does not work. Inserted the second 74HC244 in the circuit, and it works perfectly. The first part is known good.

I may have run into the one 74HC244 that does not work with TTL spec so far! 😮 But, this is why I have ordered six of them. This is also a reminder to use the recommended 74HCT244 for the buffered JTAG (Wiggler) circuit instead.