Probably also worth pointing out that the ship will have an MO and a reasonably well equipped sickbay onboard.So, how it'd actually work...
Priority 1: recover the helicopter. This means you put a bit less time in the air than the fuel suggests "just in case"; you also have something called "RAMP fuel" which means you arrive at the ship with a couple of landings worth of fuel available to you. You'll also have to account for faff the other end, so that's more fuel to stash away. In the end, burn rate etc is almost academic (and will come to rough, ready and trusted handfuls rather than an exact calculation).
Priority 2: look after the Ship. In all likelihood, the Ship will continue to close. See point 1. If not, it will loiter in the launch position.
Note - having done exactly this scenario, the limiting factor in a casevac will be either oxygen or blood supplies, given you'll be transiting for days afterwards to get to definitive medical care. In all honesty, the 20 or 30 mins you may or may not save by doing complicated maths won't even factor; the sea and weather will have a much bigger vote.
I would say it’s better to get a casualty onboard and in the care of a medical professional as quickly as possible.
Better to be a casualty in the sickbay with the doc, than be a casualty in the back of a helicopter.