I guess a lot of people before me have asked the same question about what is the dimension here. I would like to additionally ask you about what is the expected output in terms of numbers you want to see for each month and probably break it down in terms of number in the numerator and number in denominator. The more info you can provide, the easier it will be for us to play around in your sample because those are things we don't know.
I think you cannot use set analysis in your denominator because you are hoping to get it evaluated based on your dimension and set analysis is evaluated only once per chart. The expression which is working is very slow (at least for the sample), but you can give it a try