seamless patch?

No. Split the width on both edges instead of putting it all on one side. A good glue joint will be invisible when sanded and painted whereas the proposed filler will likely eventually telegraph through regardless of what is used.

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I suggest you slightly chamfer both mating edges and don't fill them. It would look like a design detail or a v-groove and not look like a "fix".

Thanks--both these suggestions are better than what I was planning.

Actually, if you were to choose the v-groove alternative (I considered it briefly, but decided against suggesting it, but reflection made me reconsider), I'd suggest looking at the proportions of the door w/ and perhaps it would make a better design feature if went that route if the whole width were at the outer edge of the two mating doors (assuming they are mating).

I'd surely suggest various alternatives to check the effect visual effect w/ several alternatives as changing stile width w/o modifying the rail size(s) can be a real shocker to the senses if not careful. Will depend strongly on the overall size of the doors and what they're going into.

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