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I developed a slide-puzzle called WrapSlide that reminds of Rubik's Cube. I am interested in determining God's number for WrapSlide. I think my initial approach is too naive and may be I should leave it to the experts.

First let me describe WrapSlide:

The main puzzle is a 6x6 grid of colored tiles which are separated into four quadrants of 3x3 tiles. When it is unmixed all the tiles in a quadrant have the same colour. A move consists of sliding either the top, bottom, left or right two quadrants of tiles 1 to 5 units horizontally or vertically. Stated differently, a move consists of sliding either the top, bottom, left of right half (consisting of 3 rows or 3 columns) relative to the other half, thus giving 4x5 possible moves to choose from. As with Rubik's cube the puzzle is to return it to its unmixed state after it is scrambled. (For the unmixed state we don't care which color goes into which quadrant)