I actually recently got told it was 'impossible' in the first wing, so exited and approached one of the desks in the main terminal, where the lady checked me in without blinking.

My advice is actually not to try and explain what you're doing, and just ask to check-in for the flight you're dropping the luggage for.

I'm not sure what the best practice is for checking-in for the b2b flights, perhaps someone who does them more frequently can advise. If f I remember correctly I had checked-in and already had mobile boarding passes for the b2b flights when I approached the desk.