Thanks for the reply, but I had already gone through those.
I did fix the problem though, using a completely different method.
I noticed that whether I ran the 32-bit installer or the 64-bit installer they each gave me the same OSE error message but referenced different files in the install folders. The 64-bit version complained about the Office32MUI and the 32-bit installer complained about the Office64MUI. So I thought maybe this was some strange conflict of architecture because I had the 64-bit version of Office installed previously. I decided to manually create the OSE service, copying the service parameters from the registry of a working computer. I rebooted, made sure my new OSE service (which didn't exist at all previously) was running, and ran the installer. It worked perfectly. I guess if you don't have OSE running it will try to use the OSE.exe file in the setup directory and that was obviously failing, so I figured I would give it a service using the OSE.exe file from the 32-bit setup directory. Odd resolution but I'm just glad its working now.