Diagnosing a gas oven's overheating problem

We've been having a problem with our gas oven. It is a Maytag oven that is at least 10 years old. Lately food has been frequently burning so I bought an oven thermometer and notice that during preheating, the thermometer reads about 75 degrees hotter than what the knob's gauge on the oven is set for.

Made some oatmeal cookies over the weekend and when the second batch went into the oven that was set at 300 in anticipation of that extra 75 degrees of heat, the thermometer was reading up over 450 degrees!

I did some browsing on appliance repair websites and also downloaded the manual for the gas oven. Both sources suggest that it could be either the thermostat or the oven door gasket. What clues do I look for to determine which it could be? If it is the oven door gasket that could be why the heat is steadily on rather than shutting off when it reaches the set temperature. Or, it could be the thermostat failing to shut down the flame when the heat reaches the set temperature.