When is the best time to pay balance on credit card, for maximum points on credit reports?

Anytime between the billing date and the due date. You get the "points" for making the payment not for the date you make the payment.

Just never being late with your monthly payments is by far the most important thing, paying early may not have any effect at all, I don't know.

It is known that keeping your balance well below the limit helps your rating, 66% helps 33% to 50% are better.

There is no such thing as maximum points, you get a bill and if you pay it before the due date then you keep your credit score, you fail to pay on time your credit score drops and your interest rate jumps about 15%

Pay off the entire balance each month.