This really gets my goat, even though I (have) never travel(led) in First.

How price-sensitive is an F customer, as opposed to a C/Y? If the food is going to cost an extra £20 per portion loaded, that's going to be about £200 extra per flight (very rough calculation there). With even 4 customers that's only an extra £50 per ticket.

Just charge extra per ticket and offer a proper F experience.