Well, I ended up peening the scythe myself. I used a mechanic's vise as my anvil. The blade had several waves in it. I flattened those against the anvil and drew out the edge. Some scalloping remains where I hammered the waves down. But it turns out that my scythe is an American scythe, with "Kelly Works" stamped near the tang. So peening isn't the appropriate way to sharpen it anyways. When I grind or file it I will take out the scalloping.
But it does cut grass. I bought a snath from
Scythe Supply custom fit to my measurements. I'm really happy with the snath. After dry fitting the handles and the blade, I saw that the handles would have to be pointed forward, which is standard for American Scythes. So I glued up the handles and took the assembly out for some test cuts. It works. Everyone talks about how you have to stop and use the whetstone often. That's not a joke. With the blade in it's current shape, it just stops mowing after several minutes. A quick sharpening with the stone and it is back in action.
My blade is pretty straight from the toe until just a few inches from the heel. That curved portion at the heel seems to do most of the cutting. But I have the blade set at the most closed angle possible. Opening the angle brings the blade to a quick stop. After I grind it I will try an open angle again and report back.