Good morning, is there any way to leak a VRFRT to a GRT without causing flopping?

Boss asked for a network configuration that used Ripv2 as an overlay and EIGRP as an underlay and we have run into(possibly) multiple issues with how the traffic will get organized. Here's what he's looking for:

• VRF DMVPN tunnels interface is visible to the global interface, but is only directing traffic through the VRF.
• Loopback interfaces are seen on the VRF interface, but are strictly for global sources(acting as ping points and other sources).
• EIGRP is strictly for the tunnel traffic in the VRF.
• There is one physical connection between all of the(3) routers.
• We are not allowed to use the IP forwarding command in the tunnel.
• We are not allowed to use a static route to direct traffic to the tunnel or physically connect.

One issue I've ran into is that in order for the tunnel traffic to pass, the port that it's connected to must be a part of the VRF. But because the physical port is a part of the global interface, we would compromise one side for the other. I'm going to try to allow a sub interface of said port into the VRF and see what that accomplishes. Are there any thoughts on this or possible solutions?