Here are some more details:
I don't mind if the data are transmitted/stored on Google's servers--as they are not confidential.
I just need to be able to have polygons on an embedded Google map that can be saved/stored and edited on a monthly basis. The end goal is the be able to answer, "In which zone does this address fall?".
I want to be able to do a local search on the page, and then see in which polygon the address falls.
The ability to set up buttons that would allow me zoom to specific polygons and print them would be a plus.
I've checked out Google Map Maker, as well as Google My Places. I think My Places might work, but I would definitely need to make some tweaks.