Hi goatpig,
Is there any foreseeable reason 0.93.3 will ever stop being able to receive transfers or sign transactions due to a Bitcoin Core version update, or for some other reason? If this version will eventually become obsolete to the point of being unusable, would that be months or years from now?
When Segregated Witness is deployed and Armory implements it, then 0.93.3 will not be able to sign SegWit transactions. This is expected to happen within a few months.
Will all future versions of Armory allow for exporting key lists so that private keys can always be kept safe in case of hard drive/wallet backup failure?
You can already do this. Just create a backup of your wallet and there is an option to export Key Lists. You can also view the key information of each address by double clicking on it and choosing "View Address Keys"