Is it possible to configure a router to do an Inside-Inside NAT? In other words, say a system on LAN 10.1.1.X sends out a packet destined for 10.1.2.2 (using class C subnet masks), can the local router be configured to NAT that address to a 10.1.1.X address and send the packet back to a device on that network?
If I understand what you're trying to achieve correctly, you're trying to allow internal hosts to access their NATed IP addresses.
The answer to the inside-inside question is not directly. However, depending on what addresses you are translating the internal hosts to and where those blocks exist on your router (on a loopback, on outside interface, or routed to null, etc..) you could take a look at implementing a modified NAT on a stick scenario. For instance, if you were to route the blocks of the outside IPs to a looped next hop, you could renat the packets that come back in the loopback interface back to the target address. Basically, what you have to create is a situation where the packets coming from your real internal IP block leave the router after being NATed to their global source IP through an outside interface and then return back through an outside interface (having a source IP of the global IP).
Take a look at this document:
Hope this helps.