Wood – How to stop the island from sliding across the floor

While I disagree with your orientation, this isn't really that hard as long as you're using a floating floor.

Start by running a line of boards across all three rooms, and orient them so they are as perpendicular as possible to all the walls. (Alternatively snap a chalk line to represent the left edge of that single line of boards.

Now in each room, measure from the left edge (or chalk line) of the board to the left hand wall. Divide that distance by the width of your boards. The remainder is the width of your starter boards in each room. Rip your boards to fit.

Start laying the boards out in the room with the most distance to the left of the line. When you get to your opening, stop - lay the boards out in the next room until they come up to the opening. Run your line of boards from the first room into the 2nd room.

Now since its a floating floor, shift the floor in the new room to align with the board sticking into the room. Click the connecting board into place, and you now have a continuously aligned run.

Repeat for room 3.

A granite slab of the size you describe and 1 1/4 inches thick would weigh about 300 pounds. A 3/4 inch slab, about 200 pounds.

This is on top of an island that may weigh 100 to 300 pounds, depending on how it is constructed. if you add some contents, the total weight with the thicker granite will probably be between 500 and 700 pounds. If people lean on it, this could add another 50 to 100 pounds of pressure.

The maximum weight of the island, top contents and dynamic pressure is probably about 800 pounds. This is divided over four (or more) support points. Each support is carrying about 200 pounds of weight. This is comparable to a good sized person standing on something the size of the area of the support point. If this were a tiny, sharp metal leg, it might well damage the surface of the floor. If it were a wide 3x6 inch board, the risk would be very small.

Tiny metal glides might do damage. Broad teflon slides, probably not. If you need to use wheels, large diameter rubber ones would probably be fine. Using the thinner granite (if it is well supported and doesn't have a significant overhang) might be better.