If you haven't had any late payments in the last year, you have already figured out a quality system to get your payments in on time. You should change nothing and continue with the method you have devised that works for you.
If you made even one late payment in the past year, you've made one too many. A single late payment on any bill can have ill effects far beyond the bill in question including a decline in your credit rating and the raising of your credit card interest rates. What you want to do is to make sure you don't have another late payment from this day forward.
In order to achieve this, start by paying your bills the day that they arrive instead of their due date. When you bring in the mail, before you read any letters from your friends, before you look through the advertisements, before you read your favorite magazine, you should sit down with the bills and write out a check for each of them if you don't have an automatic payment system set up with your bank. The next day you will put them in the mailbox and send them off. That's all you have to do to avoid all the money you have paid in late fees in the past. By committing to do this you will avoid all late fees in the future.
Even if it seems early to pay the bill, you are far better off paying it too soon than accidentally forgetting it and paying too late. By paying bills the day your receive them, you will actually save yourself both time and money. That is, you will free up time that you would have wasted if had placed the bill somewhere to pay later. You will only look at the bill once and you will never have to spend the time searching for where you placed it again.