You might be able to gut the insides out, but if I remember right the height for loading could be a pain. When we would replace the cot in the back the loading height/floor was waist high or so. That and there was usually a significant step along the back to contend with. Depending on the weight of the game you might need to eat your Wheaties!

If you can find one a vintage wagon style ambulance might be better suited to hauling pins.

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Or you can go the grim route and use a hearse.