You're a genius! Thank you everyone who helped. Hopefully others are able to benefit from your efforts.
Seems pure luck but each one makes his own luck!
All done within 1h of code surfing from scratch...
So, my recipe for Joe to find his
new E8357A HostID was:
1 - Delete or rename "c:\Program Files\Agilent\Network Analyzer\gen.lic".
2 - Kill the main app (I assume it's 835x.exe) and run it in a DOS shell with the following param:
835x.exe -954033 - The app will detect the absence of the license file and regenerate it from the EEPROM, due to that special param, using the new HostID.
4 - Then, with the new HostID, one can recalculate the new FLEXlm licenses.