How to make a custom floor transition
If you have a table saw or access to one you can mill a piece of hardwood, I would suggest oak for strength, to any dimension you want. The big box stores can sell you a piece of 2x2 oak that would work. Of course 2x2 will actually be 1 1/2 x 1 1/2 so you will first need to set your saw blade to 1 1/4" wide. Run your block through, turn it 90 degrees amd run it again, and you now have a piece 1 1/4 x 1 1/4. Depending on your where your transition meets the other floor you might not need to do the second cut and leave it at 1 1/2 x 1 1/4. Then you can set the blade to 45 degrees to ease the edge. I would not cut the 45 the entire depth (from 1 1/4 down to 0) but so that it only takes off 3/4 x 3/4, leaving 1/2" at both the hardwood floor and where it meets the tile to prevent chipping or breaking. Sand, stain and nail it down!
Man of many hats