What is the expense and difficulty of moving an exterior kitchen wall?
You'd need to get an engineer to look at it first. The biggest problems I can think of are structural -- even if the house is pier and beam, you'd need to move piers out. If it's not, you would need to dig out a new foundation. Then you have to figure out if the overhang is actually appropriate as a roof over indoor space, that moving the wall won't interfere with your joist and roof structure, and make sure that you're not interfering with your attic ventilation among other things. 

I wouldn't just call a contractor and have him start swinging a hammer, and I definitely wouldn't do this yourself. On top of that, this will definitely require a lot of permits and a stamped architectural design to be filed with your city or county.