1) find your calipers
2) measure exactly
3) post pics

And you write things like "INNER dimension of my headset/steerer tube hole is a lot nearer 1 1/8" than 1" -
If your headset - the bearings - has an 1 1/8" I.D - can take an 1 1/8" O.D steerer tube - then it's really a quite common size. An 1" quill stem would fit.