Unfortunately my offline machine is 32bit windows and I don't think I can compile.
0.92.3 had a x86 release for Windows and can sign for up to 0.95.1. I don't have these so you will have to look for them on your own.
0.93.2 offline bundles are available in x86 for Ubuntu and RPi armv7.
You should still update your Bitcoin node regardless.
One question I still have is why I couldn't broadcast from Electrum after importing my addresses to the online Electrum and the corresponding private keys to the offline Electrum? Why would my Armory setup matter at all in the case where I was using Electrum? Do the addresses not correspond to the private keys?
I do not know, I have no idea what Electrum is doing with those keys. You should ask them directly.