Silas Ware I got the photo of Silas Ware's headstone today at Prairie Home. He was an 1812 vet, but it looks like he was with a NY regiment. Don't know if that helps you at all, but the photo is on his memorial.
Now that you mention it, I think that Silas Ware (buried in the row behind John Barney) had a veteran's marker. It looks like he would have been the right age for the War of 1812. I'll go over tomorrow and snap a photo of it.
I got your photo of the Barney headstone. Unfortunately, it's a flat stone and is sinking into the ground. Prairie Home won't allow me to unbury the stone or clear it, but if you're a family member and request it, supposedly they will send their maintenance people to clear it (probably in the spring, at this point).