I don't thnk for one second you'll be able to get just the plate. Shmano aren't going to pass up the chance to sell you something you only need half of now are they?
As for getting a loose one from the lbs? I'd take a guess and say you're not the only person to fall into this hole so the liklihood of them havine one layng around is so slim.
Buy the replacement parts and learn from your mistake. If you can tighten a screw a bit tighter then it's probably tight enough. Something we've had to learn over the years and you're getting for free
The downside of home maintenance is you break things. The upside is you only make that mistake once.