Thanks for the tip J. Simon.
This workaround seems to prevent the hangups, which I only started experiencing after I installed the update to Premiere Pro CC 2015 - the same update that was supposed to fix the myriad serious bugs the original PP CC 2015 release included.
This is just a workaround though, and doesn't really address the underlying problem causing the hangups. Adobe needs to correct that issue.
As you can probably see by my response, I'm not at all happy with the buggy release of Premiere Pro CC 2015. It has caused me a LOT of problems.