How would we implement a monthly prize draw database?
It sounds like the issue is partly about how you record fact that Mary made one payment which covered entry for April + May + June and therefore you need to ensure she is in the result for your search of folks who bought a ticket for each of those months.

I would suggest doing this as a Membership for a Monthly period, and therefore some who pays for 3 months gets 3 'cycles' of Membership and therefore will be returned as being 'in the draw' for each of those months.

Then do the rest per Jaap's suggestion