You could use the space the bottle jack is in and the space in front of it. Might have to trim some plasticThe space where the jack is stowed seems a bit small for a compressor.
Maybe you can just install it across in front of the jack. Possibly on a holder with a fold-out hinge to get to the jack more easily.
This one (randomly picked) is only 190 x 96 x 142 mm.