Air-gapping means some admin will make a mistake at some point and you're back to square zero.

Much smaller chance but still.

Probably, although the technology isn't new to secure these instances. Setup a proxy that uses standard IPsec VPN tunnel into corporate. This isn't rocket science and you would only need to power a device that is completely preconfigured. That way you can create a reasonably safe environment before we even talk about application level security.