Not 100% sure if this works as never tried but you could keep the counter and add a utility meter on top with monthly cycle, the counter will just continue to increase
I suggest you try it out by setting up both a weekly and a monthly so you can see if it does what you want
The below is an example of a UM on a input_text helper counting m3 gas, where I wanted a daily view. The state is reset each night and the other one is the sum