Cisco GRE tunnel endpoint and physical i/f on different routers

I have a situation where I need to have our GRE tunnel being decaped on our edge router however the physical terminating interface for the subnet sent over the GRE tunnel is on a different router.

I have this working well on a single router, but for other reasons I now need to split it across two routers.

Ie (simplified):

WAN-------[0 edge 1]---------------[0 core 1]-----aaa.aaa.aaa.0/24

Edge is where the GRE tunnel is configured.
the aaa.aaa.aaa.0/24 network is sent to us from our ISP via the GRE tunnel
The aaa network is configured on the physical i/f on core.

Assume for now that the link between edge and core is 10.0.0.1<---->10.0.0.2

On edge I have the following

int tunnel 0
 ip unnumbered FastEthernet0
 ip mtu 1472
 tunnel source FastEthernet0
 tunnel destination xxx.xxx.xxx.xxx

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On the core I have

int fastethernet 1
 ip address aaa.aaa.aaa.1 255.255.255.0

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I need to do a couple of things (where I need help).  

Edge:
1. Tell the traffic exiting the tunnel to route to the core router.
2. Tell traffic coming in from other i/f with a source add of aaa.aaa.aaa.0/24 to go via the tunnel.

Core:
1. Tell the traffic ingress from FE1 to route over to the core router.

I tried playing around with some static routes and an route-map but could not get it working properly (ended up with some routing loops, etc).

Suggestions ?