The lower section is easily converted to roll-outs by a cabinet shop.
I'd leave the top alone.

You could get pull-outs for some of the shelves and for the rest, I would see what type of containers you can purchase that fit the space. That way, you can label the container and pull the whole thing out when you need something.

You can buy the pull out units for the bottom for about $500 from places like cabinetparts.com. There are a few places I saw them when I was looking, this site is just the one I saw first today checking prices.

By the time you factor in the time and frustration of piecing together another solution, it may be worth it!

I highly recommend the Lee Valley pullouts! Their customer service is second to none. When I ordered mine, one of the pullouts/slider bars stuck, and they sent two new ones immediately in the mail. They have various sizes. The medium one would work for your bottom cupboard. You could even fit the small into your top cupboard, and leave one or two shelves in there. (I just put light things like crackers, cereal in my upper pullouts in my pantry).

Here is a link that might be useful: medium pullout

My friend is planning to use these. She has not ordered them yet, but this was the best deal for her needs. Costco has similar ones online also.
http://www.shelvesthatslide.com/mm5/merchant.mvc?Store_Code=STS&Screen=PROD&Category_Code=SS&Product_Code=PPP5

Costo website
http://www.costco.com/Made-to-Fit-Slide-out-Shelves-For-Existing-Cabinets-By-Slide-A-Shelf%09.product.11262818.html

Most cabinet shops can make drawer boxes or pull outs for you. I used Accuride full extension drawer guides on mine.

Thanks everyone for the suggestions! Great ideas!

What about joining the two doors together in the middle and putting in a rev-a-shelf style pullout from bottom to top? Or, two separate pullouts if they don't like the idea of attaching the doors to each other?

Here is a link that might be useful: Rev-a-shelf pull-out pantry