Question on wall construction
First you need to establish that this wall is bearing or non-bearing. If you can't be 100% sure, don't start cutting.
If it is bearing, you really can't get away with anything less than what you have, and you can't turn the studs on edge.
If it isn't bearing, you probably have a couple options. You need to understand that you're going to lose some of the wall's stiffness if you cut the wall's depth in half. That will reduce the wall's ability to support shelves on the pantry side. With the base cabinet on the kitchen side, I don't think it will be much of an issue.
You might really consider using 2x6's on edge instead of 2x4's, and perhaps space them fairly close together to increase the wall's stiffness. Be sure you use very dry lumber so it stays dimensionally stable. I would definately not use 2x2's.
Another option would be light gauge steel studs. They're very stiff once sheetrocked. You can get some pretty narrow steel studs, and they're inexpensive. You won't find them at home centers, but commercial construction building suppliers should have a few options.