It sounds like no matter what, I will have to continue downloading the Bitcoin Core in order to get my coins. It doesn't sound like any getting around that, right? Even if I want to send my original Receive address (which I was sent the coins thru) I still need to wait for the core to download fully, since Armory was the initial wallet my coins were sent to? Its only at 73% now, and seems to be slowing down as it slowly progresses.
No... that is the whole point of exporting the private key(s) from Armory... you can then import (or sweep) them to another wallet like Electrum and completely forgot about Armory/Bitcoin Core.
Like I said, you don't even need Bitcoin Core installed (let alone synced) to export your keys.