You could use uppers if you aren't doing full custom. Then you'd have a 12" overhang.

That wouldn’t be at all stable. You need a 1/3 overhang to a 2/3 cabinet proportion for stability. And it needs to be securely bolted to the subfloor, and is REQUIRED to have a minimum of 2 electrical outlets. If the cabinets are less than 2/3 of the total width, it needs to be built with legs and stretcher bars, as a table, with cabinets as one side. And it still requires electrical to be designed into it.

Yes you can use an upper cabinet for an island and it can be stable. It is all about counter balance. This is mine made out of uppers. It is 27 inches with a 13 inch overhang. You can also use legs as a counter balance. Mine is movable and very stable. It would be very hard to flip. If yours will be fixed then an outlet is a nice convenience.

Even if you use legs for support, with a 12" deep upper cabinet you'd need to account for a front overhang of at least 1", plus a back cover panel--1/4" or so minimum--which means your knee space will be less than 11".

You could do something like one of these. They would be stable enough.

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How about a nice 3'x 5' island with seating on each end. A 30" 3 drawer storage cabinet in the center. Extra deep at 28" if you want it. Blum makes the self-closing slides. You can box in the living room side the entire 5' to make it look substantial from that view.

Thanks for the advice and great ideas. We have to stick with 24-27” counter width due to the size of the room. We are liking the concept that Madden, Slick suggested. Base cabinets fully supporting the full width of the counter on one half and open on one side with legs for support, on the other.

Ikea has a 15" deep base cabinet. Technically you need 14-16" overhang for a 36" high seating but I'm sure you can get by with less. The main issue is people scooching in and slamming their knees when it is too shallow.