If you're adding 35lbs of new coal to an levely fire after shaking it, you should be able to slow it down by reducing the input air more than you do now. Sure the heat will be lower, but the stove won't burn up the load overnite.
you probably need a larger stove, but for now try to reduce the stove temp to 300 with the draft control and see how long it burns
Is ther a baffle or something to restrict the the exaust from a direct shot out of the stove.
Also you could adjust the baro for somewhat less draft to keep more heat in the stove.