Don't use the mid term, as it is a long walk with no buses. Also it is now only 15 minutes free. Better to be dropped off in the long term car park and ask to be dropped off by a car park bus stop for departing passengers. The driver will get 1 hours free parking.
https://www.london-luton.co.uk/parki...ampaign=glocal
Regarding being dropped off in the multi story. They would have to only use car park 1 and the driver would have to make his way to the priority parking office to register his vehicle, showing I guess the blue badge. Too much faff, I doubt the driver would do it.
https://www.london-luton.co.uk/speci...dropoff-pickup.
The other option is to pay the £5 for the drop off zone.