Doing full kitchen rehab DIY. Part of plan is 3mm granite top, 6' long, with 12" overhang coming off a 12" cabinet.

Idea to avoid granite breaking and/or the entire assembly tipping over is to use a flat steel sheet covering the entire area less 4" from front/side granite edge, screwed into the cabinet tops and extended into the wall behind the cabinets. The plate will be cut to go around, and extend between, studs 1-2 inches. Studs will be notched directly above the plate and a horizontal steel bar running between/screwed to the studs will sit on top of the plate end. The bar (hopefully) will keep the back end of the plate from tipping upward. The cabs will be screwed at base and top to the wall studs.

tipping concern because I can't get larger ratio of cabinet support to overhang. I've seen steel plates recomended, but not the in-wall bar idea. Can't use corbles cuz cabs are full face and need to open the doors.

Will this work? Is 1/4" steel ok? Trying to avoid weight of 1/2" (already adding floor weight with porcelean tile).