Returning player looking for specific assistance

I haven’t heard of any such corporations, but jump fuel doesn’t seem to be the only thing you need to escape. You’ll also need a cyno.

If you already have a second character you could maybe do both the cyno and fuel with one character by using mobile cynosural beacons where you first place the cyno at a nearby NPC station within range of the Carrier and then warp to the Carrier’s system to deliver fuel.

Just be careful not to post this on your carrier pilot.