Quicktime 7.1.6 causes browser crashes or bad behavior - any fix?

I have found that any attempt to view Quicktime content within either Internet Explorer 6.0SP1 or Firefox 2.0.0.11 results in bad behavior.

In the case of Firefox (my default browser), Quicktime 7.1.6 will either cause Firefox to crash entirely, or a message stating that a plugin has performed an illegal operation will appear. If the plugin message appears, the browser won't crash.

Over in Internet Explorer 6, Quicktime won't really crash the browser, but the IEXPLORE.EXE process can be seen chewing up all kinds of processor time in Task Manager.

I don't think this is a problem specific to just one computer or configuration. I have a number of systems in various locations that have the same exact problem. As far as I can tell, the only common denominator is the fact that the systems are running Windows 2000 and Quicktime 7.1.6. (So far as I know, QT 7.1.6 is the last version for Windows 2000 users. I think Apple dropped support in the newer versions.)

I did do some looking around, and while others have encountered this problem, there doesn't seem to be any definitive fix.