Why u like to do static NATing ? As you can access this server with the same IP 192.168.1.1 from inside network (10.1.1.0) also. Only thing u have to do is create proper nat and global statements for this.
nat (inside) 2 10.1.1.0 255.255.255.0
global (dmz) 2 192.168.1.4-192.168.1.250 netmask 255.255.255.0
Remember that IP pool u r defining in global statement should not be used in DMZ network.