Is there a way to get an Airport Extreme to coexist with a second router offering VPN?
Yes, there is. You set up your other router as the default gateway for the Airport Extreme, put the Airport extreme in bridging mode via the Airport Utility.

The new router will be connected to your ISP, and have the VPN tunnel set up, depending on which model you choose you will be limited as to what type of tunnel you can set up (GRE, IPSec) or something else, in the case of routers such as FritzBox (which can only set up VPN tunnels to other FritzBox routers.

I would recommend the cheapest 800 series router from CISCO. 

Or you could also  run pfSense virtually or on a stand alone box which will provide VPN functionality you require.