Is it possible to change the default gateway of the DHCP server side of an Airport Extreme
Just configure the AP in Bridge-mode so it's running DHCPD and distributing addresses.

Then, on the internet tab configure it statically and give it the high IP you want. You probably want to configure the range to be 1-253.

Personally, I find Airport Utility 5.6 to be better than the 6+ versions. You might want to give that a try too (see here for how to get it).