How can I bake these cheese and pimento rolls so they're not gummy inside?
When you did different filings before, I suspect they took less heating up, and that your cheesy filling is stopping the internal temperature getting as high as it should. This could be because the cheese goes on fridge cold and has a higher heat capacity than whatever you used before. The water content of the pimentos and cheese may also not help. 

In terms of a solution you need longer for the heat to reach the middle. I doubt just starting with the cheese at room temperature would be enough. To avoid browning too much you'll need to reduce the oven temperature, but not by too much or the pastry will be too pale and again not cooked through. This will take a little experimenting, especially if you take the approach of preheating the oven to the current recommended temperature and reducing the temperature when you put the food in (which can work well but depends on how well your oven is insulated). I work in Celsius but rounding my guess you might turn it down to 320F when you put them in.