Simple and affordable way to make carriers both fuel efficient and possibly jump capable is to do commercial engines and commercial jump drives regardless of if the carrier is a military craft or not.
I do this sometimes with escort carriers and often with super large carriers for which I can't afford to create military jump drives so I need a commercial jump-drive. Their role is simply to act as a giant floating fighter base and will move at the same speed of my fleet support ships.
Cheap engines on a carrier make them really cheap to give them long deployment times, maintenance cycles and with being fuel efficient can operate far from home with impunity. Low speed obviously comes with its own disadvantages but you can't get everything.