Hi,
If I had understand your problem correctly, you need the following configuration:
interface gi1/0/6
ip address 10.aaa.bbb.$ 255.255.255.0 // NOTE: I have changed this address to bbb net
ip nat inside
interface gi1/0/1
ip address 10.aaa.ccc.$ 255.255.255.0
ip nat outside
ip nat outside source static 10.aaa.ccc.y 10.aaa.bbb.x // Changed the order of addresses
ip route 10.aaa.bbb.x 255.255.255.255 10.aaa.ccc.y
Hosts on bbb network must access server 10.aaa.ccc.y as 10.aaa.bbb.x.
The static route is needed because 10.aaa.bbb.0/24 is associated with gi1/0/6 interface.
I hope this could help your configuration.
Best regards,
Pedro Lereno