Pan size and cream pull candy

The higher the temperature, the harder the caramel. That is basically the whole story. So I think what is happening to you is that the caramel in the middle is still going up in temperature due to residual heat, while the stuff at the sides cools down quickly because it can vent heat through the pan to the outside world. Have you checked the calibration on your thermometer? In any case, I think the things you can try are (1) cook to a slightly lower final temperature (back down a couple degrees at a time) and (2) set the pan over a tray of ice to cool it more evenly. Also, be sure to do a really good job of that final stir before pouring into the tray.

I noticed that you're stirring constantly. Generally with candy you want to stir as little as possible, since it causes sugar crystals to form in the syrup. In addition to making the candy grainier, they reduce the overall lifespan- even after the candy has cooled the (larger) crystals will continue to grow, causing the candy to slowly revert back into flavoured sugar.

Once the sugar is fully dissolved, you want to disturb it as little as possible. You will still have to do some stirring, otherwise the milk solids will burn. It'll help a bit to mix in the corn syrup at the same time as the sugar. Corn syrup is an invert sugar, meaning it gets in the way of crystallization and slows it down. If your caramel is still coming out grainy, try adding half a teaspoon of lemon juice. Your candy will be slightly gummier, but the acid in the lemon will inhibit crystallization and reduce the graininess.