Tahoka,
I stopped attempting to use TiddlyWiki single file in IE some time ago (IE as a whole actualy) - preferring FireFox, perhaps others will have some advice.
However if the Wiki can be accessed at an IP address your are unlikely to have the same problem. Can you use nodejs, Bob even the bob.exe to server your wikis?, you can then access it at the
127.0.0.1:8080\wikiname address and the server does the saving for you?
If you can not install anything at work, then wait for some IE advice.
Regards
Tony