The US models of the new OFA and RS (UEI) remotes DO NOT have more learning memory than the Cinema 7+.

The 15-2133 supports a 4K eeprom, but is sold with a 2K. Someone has soldered a bigger eeprom on his 15-2133 and gotten double the usual learning memory.

I expect OFA will be selling 4K eeprom versions of a related remote in the near future (that might even be what the European remote similar to the 15-2133 is now; I haven't heard anything yet that confirms its eeprom size one way or the other).

With or without the larger eeprom, you're better off using JP1 to get a device upgrade for the Outlaw rather than learning all the signals. Done as a device upgrade rather than a bunch of learned signals, there's plenty of room in a 2K eeprom for that device and much more.