Do you really have room for something 36" wide? You say you've got 35.5" and the Ikea cabs are actually about 35 and 7/8". (It might be worth taking out one of those walls to get the room,
FYI
. I doubt they're both (if either) weight bearing.)
Assuming you have the room, you could do a 36" drawer stack with several 36" wide plus two deep cabs meant to go over a refridgerator, one 24" high and one 15" high, for a total of 75" in height with legs under the drawer unit. Each of the fridge cabs can be modified with the doors turned to pullout fronts. The fridge cabs hang on the wall rail and do best with side support, which you'll have available. Each one would absolutely require its own rail, securely attached to studs.
If you can't squeeze out a full 36", 30" plus room for sliding broom closet pullout is not such a terrible situation. You'll find the internal drawers are a huge advantage and you'll get more out of your space than you previously had.
Hope this helps!
