In my old car I had the changer under the passenger seat, great place.
Easy magazine change, you can grab it as you sit in the driver seat.
No valuable space occupied
So that was the way to go on the Cooper.
It could bee done, but then I have to compromise the seat travel backwards or the floor space for the back pax.
Then I discovered the polystyrene /tempex plate under the seat
Hidden under the carpet there is a big polystyrene plate between the seatrails.
Armed with a knife and saw I cut the carpet like a " U " , cut a wig/triangle form out of the plate, drop the carpet back and in goes the changer

(Seat max aft)

(Seat max fwd)
Now the seat has its full travel and max floor space for back pax (but who cares..)