Nice Militia Plate!
Pulling from memory, (I'm not looking in my reference books), I believe that style dates from around the 1820's. These were apparently in use for a couple decades, as they've turned up at sites nearly into the 1860's. Some have attributed these as far back as the War of 1812, but I'm not of the opinion they are quite that early. Your example is missing the attachment loop on the back, made of brass wire.
In regards to cleaning, your find looks quite good as is! The green is actually not detracting from the piece. Any attempt to remove the green could possibly do more damage than good. My vote is to leave the cleaning at the point you are at now. A possible straightening of the bent corner by an expert in relic restoration, is about all the piece needs (in fact, the missing loop could be attached as well). Did you carefully check the hole for the wire loop? Since these bent wire pieces were simply attached with solder, we commonly see examples where the dissimilar metals will separate after a century or two in the ground.
Good Find!
CC Hunter