So a little more information - I was able to sift through the installation logs and found these two lines, one after the other:

INSTALLMESSAGE_INFO Message: CustomAction VerifyIfBetaVersionIsInstalled returned actual error code 1157 (note this may not be 100% accurate if translation happened inside sandbox)
INSTALLMESSAGE_ERROR Message: Error 1723.There is a problem with this Windows Installer package. A DLL required for this install to complete could not be run. Contact your support personnel or package vendor. Action VerifyIfBetaVersionIsInstalled, entry: VerifyIfBetaVersionIsInstalled, library: C:\WINDOWS\Installer\MSI8494.tmp

So my assumption is the 'VerifyIfBetaVersionIsInstalled' command is what's actually causing the error in the MSI installer. I'm going to wipe out the temp folder and reset its permissions, then see if that makes any difference - I suspect the fact I can't change permissions/access in the usual manner means something funky is going on with that particular folder.