I divided my run in half, and sowed "ceral rye", if its warm enough, it will germinate in 4-5 days, and be about 4 inches tall in another 4 days. It also will keep growing until 33 degrees. cost 24.00 for 50#, and will go a long ways
it wont take very much more materials to build a 4X8, and you wont waste nearly as much
(plywd is 4X8), by the way I am straight west of you just across the state line. My first coop is a 4X6, and I realized I could have build a 4X8 just as easy, now Im gathering materials for a 8X12, lol