Hamburg Airport to Frankfurt-Hahn Airport: 610 km, about 6h 08, one car, no changes. Most people making this journey were rebooked onto it, so the pickup is set from the flight you actually landed on and the drop-off from the one you now have to catch.
The pickup is driven by your inbound flight number: the driver watches the actual landing time and waits 60 minutes free after touchdown, which is what a diverted or delayed arrival needs. At the far end the drop-off is at the terminal door, not the car park. Tell us the departing flight at booking and the schedule is worked backwards from its check-in deadline rather than forwards from a convenient departure. We run the same journey to Frankfurt Airport, priced the same way.
Luggage stays in the car for the whole 6h 08, which is the single biggest practical difference from any rail route: nothing is lifted onto a train at Hamburg Airport, off it again at the interchange, or onto a second one for the run into Frankfurt-Hahn Airport. If the airline has rebooked you and is reimbursing ground transport, the invoice shows the route, the date and the fare in a form an airline will accept.