How do I transition from a wood floor to tile that has a 1-1/4" height difference?
Find a custom wood molding shop in your area (there will be one) and have them custom bevel a piece of 1 1/4" oak in a width that suits your fancy, then stain and varnish it. It will be more easily accomplished than you think, and the custom milling charge you will pay will be worth every penny.

I might just butt a narrow piece of 1 1/4" oak right up to the tile, or maybe 1 1/4" quarter-round (if you can find it). Better to just know you have to step up/down than to have a weird sloped transition.