Spacing when transitioning tile size
At a glance, this might work... you'd line up the outsides of the 3x3 grid with your 18" tile. You'd have about a 1/8" grout line inside the 3x3 grid. You'd maintain the 1/4" grout line around the 3x3.

Don't take my word for it, though: lay it out on the ground and see what you (and any other people with veto power that have to live with it) think.

Oh, and depending on the grout you choose, you might have to switch from sanded to unsanded. Just check the instructions.