Thanks, E, but I can't imagine the amount of time it would take me to router a dozen treads like that.
I had a flooring installer over and explained the situation to him, he agreed that while solid 1 1/16th treads were a bit much, using 3/4" wood on the treads should be fine. Honestly, every single application of additional hardwood to treads (as opposed to replacement of treads) must have encountered this same quandary. Assuming that the stairs were of even rise before adding the treads (not necessarily a valid assumption), unless you were willing to add the same height of materials to every level of the house that the stairs touch, you'll be out of whack somewhere, either too short or too tall on a rise.
I'm going to go ahead and install 3/4" wood on all the treads, and to soften the height difference from the ceramic floor to the first tread, I'm going to get a small, thick, oriental style rug to put on the ceramic tile at the bottom of the stairs. These carpets are usually 1/2" - 3/4" thick, so that should even everything out.
This got me thinking - how does the code relate to stairs with carpeting & the height of carpets. I measured my pad & carpet that were on the steps, and it worked out to about 1 1/8" high. Even compressed, it was a half inch high. So I'm guessing I've been out of code all these years. Never noticed a problem.
Here's a simple image I made to show what I was talking about.
Thanks to everyone who offered suggestions. This is a very helpful site.