You could make extended frames that attach on top of the existing cabinetry. I think a pocket hole jig like the Kreg would work great. Look to Ana White's blog for lots and lots of plans that show how to use the kreg tool. The manufacturer videos are pretty good too.
Then, you could order or make new doors that are sized for the full height. Alternatively, you could make or order doors sized just for the top cubby as an addition.
Finish off by adding a panel on the exposed side. You will also want to put a sheet of masonite/hardboard on the current cabinet tops, to keep items from getting trapped.
Buy a ladder, you will need it to get anything down!