Paper mats: I’m sure the Seklema mats are great, but I’ve had success using just a piece of plywood and Krylon Easy-Tack adhesive spray.
Corner burning: corner burns happen because the head has to decelerate and accelerate to make the turn and the laser power isn’t adjusted accordingly. I found that I could reduce or eliminate corner charring by slowing down the speed and lowering the power accordingly. The acceleration changes are smaller.