Interesting idea. My only concern is that the blocks would be super huge... since the FQ would be 18" x 18", so the first block would be 54" x 54" or so, then cut up and reassembled, 50" x 50" (rounding now), which just seems really, really big.
I could see it working better if you cut the FQs into 9" squares (4 from each), but 18" just seems very very big. Good idea though - no reason to just use the tiny 5" squares! (that's what I use)