I never had a problem with the Mr Tuffy strips staying centered as long as I kept the tires within the recommend PSI range. I used them in Utah for around eight years. I no longer needed them when I moved and I found tires that do the same or better job of flat protection since then. I currently use the Schwalbe Pick-Up in a 26X2.15.
The 26X2.15 Schwalbe Pick-Up tires are the largest volume tire that fits my bicycle.