With the tile edges not being exactly even. I would try and create a transition that would overlay the tile flooring. And be nailed into the hardwood.
The easiest design is to have a mill shop create this transition. the tapered edges should be no thiner than 1/8" thick to avoid splintering. I would overlap the tile and be sure the lip is resting on it to give it supporting strength.
If you are interested in creating your own transition rather than contracting that out. I have other ideas. Though it should cost you less than 50 bucks to have someone else do it.
Might this be a bit thin to be strong enough? I was thinking along the same lines but considered thickness to be an issue..
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