The triangular iron item you have is, I believe, not actually a riding stirrup. The shape, style, and size, is more consistent with a functional iron hardware piece, for attachment of a chain to a beam. Seems more like a wagon part, farming piece, or logging application. At the moment I cannot place my finger on the idea, yet I'm quite certain similar pieces are something I have dug and/or seen over the years.
Hopefully some of our other knowledgeable forum members will drop by, with a more precise identification.
CC Hunter