I would order (or see if they are available locally) two short lally columns and put one at the back of the counter overhang and the other one at the front. If you bridge them with an appropriately sized length of 2 by 4 lumber between the top of the columns and the bottom of the quartz counter overhang, you should be able to get good support for the 3 inches of counter and still have it be easily removable if need be.

That should allow you to put a piece of cover panel in front to hide the columns and make it look clean.

Simply screw a 3/4" x 3/4" cleat to the refrigerator panel and one from the panel to the sink base cabinet on the rear wall. It will be fine.

Thank you for your suggestions! Those both sound like easy solutions!

I'd use Joe's suggestion and add a 3" trim piece on the front, to cover the gap. (DW return panel.)

Okay, thanks! You all are great!