Hello,
you can route EIGRP over GRE. In fact there is a document on CCO that discusses it in conjunction with DMVPN: "Configuring Dynamic Multipoint VPN Using GRE Over IPSec With EIGRP, NAT, and CBAC"
http://www.cisco.com/en/US/tech/tk583/tk372/technologies_configuration_example09186a00801982ae.shtml
You might want to have a look at this.
As a general remark: make sure the tunnel destination is not dynamically learned through the Tunnel. This recursive routing condition can lead to constant flapping of tunnel interfaces.
The MPLS VPN portion is not that important to your solution, because as long as it is unicast IP traffic the provider will not have a problem delivering it.
Hope this helps! Please rate all posts.
Martin