In case anybody else runs into it, I managed to solve the problem by doing the following:
The next time I ran the NewGen World Editor it performed a first-time launch and did not crash.
No problems occurred during second or third launch either.
- Uninstall Warcraft III
- Go to the Registry Editor (regedit) and delete the key HKEY_CURRENT_USER\Software\Blizzard Entertainment\WorldEdit
- Reinstall Warcraft III and The Frozen Throne
The next time I ran the NewGen World Editor it performed a first-time launch and did not crash.
No problems occurred during second or third launch either.