Anyway, I register the product and restart TCC a few times - always from the USB key, and always it comes up registered. So far so good.
Then I plug in ANOTHER, removable USB key, and copy the TCMD13 folder from the first USB key to the second one, including the registration key file.
In the current TCC session (first USB key) type: SHRALIAS /U & EXIT.
Start TCC from the SECOND USB key. It says that my evaluation period has expired. So it seems like the portable folder is bound to the first USB key only.
WAD -- the registration key is bound to the USB drive where it was installed. (Otherwise, you'd have a universal version which could run on a billion different machines -- which some people would like, but wouldn't be very good news for JP Software.)