put a static default route in your core EIGRP router and use:
R(config)# ip route 0.0.0.0 0.0.0.0 xxx.xxx.xxx.xxx
R(config-router)# redistribute static
if for some reason, the core router does not know of all the networks a host must get too, you may want to think of putting the static route elsewhere or in a few select routers.
