I really like your idea of using the tile pattern to do this... I have a really hard time doing "random" pieces. I've done 2 round stepping stones by randomly laying scraps and they seemed to take forever and I had to do both of them in multiple sittings so the frustration level didn't get too high
I get up early so I cut up these pieces real early in the day. Took the pattern to the living room, laid it out on the coffee table and spread out the pieces. Left it there all day and as I walked by or was watching TV that evening as I noticed two of the same glass the same next to each other, I just moved it around like a jig saw puzzle. Even my husband got into the "game". By the end of the day, we had a "random" pattern.
I don't do random well either.
another way to look at pieces and find things that are "off" is to use a peep hole -- the same thing you would install in a door. a quilting friend of my mom's suggested it to her and it works... just look at the piece through the peep hole and if something isn't right, it kind of pops out at you -- not sure how it works, just know that it does