Make Views pager count rows, not items?
It sounds like you need a view of views. Try the module Views Field View.

I don't know if this is doable. But this is what I will investigate:

In your primary view you must create a month only field, and page on that. Then in your secondary view (which will become a field of the first view, and to which you pass the month as context) you return the dates for the passed in context of the month. You will then end up with a multi-value date field in the first view. You might have to do some rewriting of output  (Views PHP?) to get the dates as text or integer fields.

And if you get it right, remember to employ views caching as Views Field View adds a lot of database queries.