Is there a way I can NAT routing updates?

I have a need to connect to a customer site and exchange BGP with the customer. This is all fine. But the customer has all RFC space addressing and won't/can't NAT. I don't have an issue with natting their addresses as they come into our network but I want to keep dynamic routing intact since They will have multiple connections into our network for redunancy. Their RFC addressing conflicts with what we have internally so we can't redistribute their routes into our internal network unless somehow these routes they deliver to us via BGP can be NAT'd. (They can receive our routes since we will only be redistributing our public networks to them). Can this type of NAT'ng be done?

If routing updates can't be natted, I was thinking that I can just add static routes pointing to their dynamic routes and redistribute those statics into our internal network. If for some reason we lose a dynamic route from them, I'm hoping that maybe the dynamic route will be deleted from the routing table.

i.e.

Let's say they deliver a route to us like:

B 10.10.0.0/16 [20/2] via 192.168.10.4, 2w4d

This route conflicts with a network in our internal network.

So I add the following static route:

ip route 10.40.0.0 255.255.0.0 10.10.0.0

and redistribute this route internally.

Now I just nat anything coming in as 10.10.0.0 to 10.40.0.0.

If I lose the 10.10.0.0 route from the customer, my static route should go away as well. I would much rather just be able to NAT the route. But....

Any ideas, suggestions?

Thanks for your help!