If you insulate as pictured you reduce the cold surface area and prevent some passage of cold air between the boards which could improve things a good bit but you still have a cold bridge from the joists to the floor.
I think you would achieve a greater gain by laying a floating floor with a continuous layer of solid insulation boards over the existing floorboards, topped by a plywood/engineered wood layer, then your flooring. Obviously you lose some height from your kitchen and raising the floor level might mean significant interior work to accomodate. Less disruptively you could use a thinner layer of insulating underlay in addition to your insulation between the joists. Encapsulating the joists in some form of insulation as well as between them would be another way but it would be an awful job to do unless you spray foam insulation on them.
You should have the vapour control layer on the warm side of the floor and a breather membrane on the exterior.