This has nothing to do with NATting, this is plain old fashioned routing that is bugging you.
When you try to access 1.1.1.2 from 1.1.1.1 it will just do an ARP to the network the host is in. Now when you use the network 1.1.1.x on a DMZ this means you have a route for it from the internet and you have no need for Proxy ARP and you can use manual NAT.
However in this case you will need to tell the FW that it needs to act as if it has IP 1.1.1.2 on it's DMZ interface, this is done by the aid of Proxy ARP in clish:
add arp proxy 1pv4-address 1.1.1.2 interface <DMZ>
At the spot of <DMZ> you fill the actual interface for network 1.1.1.x
Regards, Maarten