I'd like to use EIGRP or OSPF on the DMVPN, but I'd like the DMVPN to serve as a backup for our existing MPLS network which is using BGP. I've thought about creating a second DMVPN over the MPLS and ...

So, BGP removes the default. This change propagates through BGP to the MPLS providers. The carrier’s MPLS backbone picks a default route from another hub site, reconverges, and Internet traffic flows ...