CNC Shield V3 and step motor controls
I agree with Wesley Lee, in that a linear regulator is not the proper power source for your application.  Although there are newer and more efficient linear regulators that would work in your situation, you would be better off using a higher current switching regulator with a fairly large capacitor on the output.

Obviously, you should be measuring the current used in each branch of your circuit to see exactly what the average/peak current draw is in each segment of your circuit.  This would give you an accurate account of the actual requirements, and give you an idea where to further investigate in order to improve your circuit design.

As stated previously, as long as your components can handle the increased current, you could just throw a much larger current supply at the circuit, and hope that it either works, or blows something out.  Current limited bench power supplies are your friend, in this situation.

Of course, all of this can be worked out using math, but it would likely be faster to just micro analyze your circuit while in operation using the appropriate test equipment, since you have already determined that it is already somewhat working.