Are you actually positive. I can't outfit mine, and I'm one jump in any of my owned ships, and the fleet carrier from the system I bought it and I can't outfit additional services.
Huh, odd. I bought mine in Skeggiko O, but it spawned in LHS 2435. Despite that, I was still able to outfit it through the carrier vendor in Skegg, without actually having to be on the carrier.Correct, you cannot make any changes or even purchase any outfitting outside an admin system. You can't even change services you have bought, only disable them.
Try jumping your carrier into a nearby system, then going to the selling station and try to outfit it using the original vendor. That might help. If not, you might want to relog and submit a bug report.