Should I install bracing behind drywall for upper cabinets

Is cutting out the flooring where the cabinets will be not an option? You don't mention it, so maybe there's a reason, but that's the method that would get you the best attachment for your cabinets, while still allowing the flooring to float and move as it's designed. You could make these cuts with a circular saw set to just the right depth.

For the peninsula, I believe cutting out the flooring is your only option. If you try to attach it through the flooring, you're either going to 1) pull it too tight to the flooring so the flooring can't float, or 2) not fasten it tightly enough and it's going to creak and move every time someone leans on the counter.

You need something like these Heavy Duty Cabinet Hangers:

components http://www.screwmaster.co.uk/ekmps/shops/screwmaster/images/pair-of-heavy-duty-cabinet-hangers-260kg-load-capacity-for-kitchen-wall-units-57-p.jpg

The metal plates at the top screw to the wall, the hook like things in the middle screw to the inside of the cabinet and the plastic covers them up.

in place http://www.screwmaster.co.uk/ekmps/shops/screwmaster/images/pair-of-heavy-duty-cabinet-hangers-260kg-load-capacity-for-kitchen-wall-units-%5B3%5D-57-p.jpg

You do need to cut a hole in the backing for the hook, but the plastic will hide these as well.