2-4 children per Jewish family? Where did you get that stat? And what do you mean by a “Jewish family”?
Modern Orthodox families typically have 3-4 children; yeshivish families have 7-8. Of course you have your 12s and 2s, but it averages out. My husband wants 3; I want 4; of course it is ultimately in Hashem’s hands! We will have as many children as He blesses us with, i”yh.
Shul membership fees can vary widely. $1000 is, I think, on the high end of the standard range. But no shul will turn you away if you really cannot afford the full fee. I know they have special arrangements with families that need it. And you can certainly help out the shul in other ways as a volunteer. My home shul, for instance, has a policy that each adult member must sponsor Kiddush once a year (this means twice a year for a married couple), but if there are financial issues, the shul will pay for it. They just want families to “sponsor” by shopping for the food and helping to set up/clean up the Kiddush so that the burden doesn’t fall on the same people to set up and clean up week after week.
We stayed with a Chabad family for Shabbos recently that has eleven children ranging in age from three months to 18 years. The rebbetzin told me she has seen so many women come to her and say they wish they had had more children and that from her perspective, you just have to have the children and the parnassah will come. I thought that was very brave and although I’m not sure I could handle a family of 13, I admire her for it.