You could drill new holes in the center of your mounting plate in a vertical line say 2" from top and bottom, use 3" screws into just one stud and call it good. I'm certain that would hold 100 lbs or more. If you wanted more, which I don't think you need, you could use 1/4 or 3/8ths by 3 inch lag screws, pre drill and use a ratchet to drive them in. You could paint the heads black with some rustoleum to match if they showed.

OR, you could mount a 12 x 12" piece of wood to the wall using the above method and then mount your plate to that piece as per the instructions.