Can't download sketches via USB-serial converter onto 644P, even with a bootloader

No, that's normal. If the bootloader does see "proper" commands to upload a new sketch, it will start running whatever sketch is already present, after a little more than one second. So it sounds like your RESET is OK.

CH340G's RX goes to the Atmega644p'S TX, and vice versa, right?

Yes, that should be correct.