graft onto a cherry tree?

I have a mature but unproductive cherry tree in my back garden in southern England (zone 9)

The cherries are small and tasteless with a low fruit:seed ratio.

Can I prune/pollard it and then graft on some branches from a more productive variety of cherries?
Has anyone tried this?

The trunk is 40cm in diameter at chest height and the top of the crown is higher than a two-storey house.

The technique you are searching around for is called rind grafting. Search on that and you may get some useful ideas.