Swapping Zend Core and the beta of Zend Core 2 around, I got my computer to a state where DB2 would not run, would not uninstall, and would not reinstall. Zend had hosed my DLLs/registry/environment in some unknown way.

Digging around turned up that, for times when the graphical uninstaller fails, there is a command line one that always works:
db2unins - Uninstall DB2 database product command

I’m not entirely clear on why they didn’t just fix the graphical uninstaller instead of writing a second one. Still, db2unins -f cleaned my system, allowing me to reinstall DB2 and remap existing databases.