I'm remodeling a bathroom and had to install a new subfloor. I installed 1/2inch hardibacker above the new subfloor which has raised the floor from how high it was originally.

What's the best way to transition tile to the hardwood in the door threshold?

Origonally there was a stone threshold, but my local tile shop doesn't sell stone threshold that reduces. I want to avoid using a metal reducer.

I think my options are:
1) Keep looking for a custom threshold that reduces 1/2" are these even available?
2) Install a regular straight stone threshold but angle it by building up the high side with more thinset.
3) Try to do something with wood for the threshold that would match my existing wood floor.

Thoughts? Suggestions? The pictures included show the old threshold as an example to show the height difference.