With company profiles and config.php transferred, logging in gets the expected [backup DB] [UPGRADE] lines. Running the upgrade pops back to UpgradeDatabase.php, but doesn't seem to do anything except change it's information message, and pop up a new tab.
I ran the >4.07 sql scripts, and logged in, and everything was fine. Looks like the UPGRAYYDDE (that's with a dubble D for a double dose of dumb) has a little boo-boo though.
I will re-create the travesty (on the real server version) and play with firebug to see what is going on for real.
4.07.8 ~ 4.08.1 upgrade