I know I've said this many times in various posts, but if you want to be able to actually sit normally at an island/peninsula, you need the 15". 12" may be fine for people with short legs but it usually means you either have to sit sideways slightly or you "straddle" the island/peninsula to fit. Neither of which, to me, is comfortable for very long. We have friends w/a 12" overhang on their peninsula and I find it uncomfortable to sit for any length of time if I'm trying to sit at it to eat or talk to someone in the kitchen. It's not bad at parties where I turn the stool around so I'm facing outside the kitchen (i.e, sideways to the peninsula). My DH won't sit there at all b/c it's just too uncomfortable. We put in a 15" overhang which seems perfect for me and my DH only has to "straddle" a very small bit...3" doesn't seem like much, but it makes a big difference! If you don't have the room, you don't have it. But if you have it, I strongly suggest going with the NKBA recommendations (see link below). Here is a link that might be useful: NKBA: 9: Seating Clearance

Thanks much for all the comments - sorry the excel layout leaves a lot to be desired to understand the flow to the rest of the house and the exterior - which is pretty important. I'll try to lay something out - but basically, the backdoor comes in off the driveway which is at say elevation 0, then there is a first step down into the first part of back yard, about where the steps down are from the EIK that takes you down to -4...to a lower bluestone patio that goes into a walkout basement right below the butler pantry. Then, the backyard slopes down yet again another 4 get to -8 total to the right of the end of the house. I will draw up. What do you think right min. size is for a 4-top round EIK? In my "excel" lingo, the black rectangles are doorways and the orange are windows, so the thought was to create a floor to ceiling glassed in EIK, which is the best view of the backyard. (Top of plan is north, so is going to be south facing which is a concern). The door out of the EIK is the secondary access to the backyard - and the grill. Good point about the location of the refrigerator - thanks again for all comments...

I find the bumpout charming and wouldn't get rid of it. I would sooner get rid of extra pots and pans and such, so I wouldn't need as much cabinet space!

A new wider countertop is your only option. You need 12" of overhang. In theory you could remove the cabinets and completely rebuild them to a 12" depth (no idea why anyone would go through that effort). But then the cabinets would not be deep enough relative to width of the top. You could buy new cabinets in a 12" depth, but again not deep enough for the width of the countertop. If the stools are already in that space taking up room, a wider countertop is likely not going to make any difference, but you need to leave at least 36" from the edge of the countertop to the nearest obstruction on that side.