Design question: How best to make EIGRP route a priority over External BGP?

[esa_fresa]

We have two datacenters, each with an ASA that has numerous tunnels to peers on the internet. The routes for the tunnels are redistributed like this:

ASA-DC1  ---> SWI-DC1 ---> SWI-DC2 ---> ASA-DC2

.................EIGRP............External BGP........EIGRP..............

When DC1 has internet access, we'd like all tunnel routes to go through ASA-DC1, even if they pass through SWI-DC2. The failover route should be to ASA-DC2. I can think of a number of ways to do this but I'm looking for input for the best way. A big problem is that I think routes will be looped if we just redistribute like normal, since eBGP has a lower AD than EIGRP.

[esa_fresa]

So one of the solutions we're looking at uses AD to choose the route. We have a concern with this though, as follows...

If the VPN routes go down on ASA1 then they will disappear from the EIGRP table on SW1. This will make the BGP route (with AD modified to 91) from SW2 the best path, and SW1 will send traffic there. BUT I don't think the BGP update will be sent as fast, so for a time SW2 will be sending back to SW1. Is there a way to tell SW1 to share its route update immediately with SW2 after it loses the VPN routes in EIGRP?