You are asking a good question rather than rushing in and spending precious time,
4 rods is 110 square yards, so not enormous as you say.That means a lot of edge in proportion to middle. I would worry about marestail creeping in from the edges, even if you succeeded with mulching through a year of membraine.
If its good soil and you can afford the wait, and the membrane, and if the council keep the edges mown regularly, it may be worth it, do make those points as they are not often appreciated.
