Custom Wood to Tile Transition Needed
I had a stone threshold fabricated for about $50. I went to a local tile shop & looked through their scraps.
I chose one that contrasted with my floor, to warn of the trip hazard. (they didn't have black & yellow stripes).
They told me to make an exact template of the shape I needed out of heavy paper. It was a good thing, because it turned out to be a trapezoid.
I think you could also make it of wood, by stacking layers. To get 1-3/8", you could buy a 1x__ (that is actually 3/4" thick), and use other wood under it. You will need to round the edge with a router, sander, file, or plane. A board that wide will glue down better than the narrow transitions being offered nowadays.