It depends if you take the upper or lower Antelope Canyon. I did the lower one which apparently is a bit more tolerant for light entrance. Besides on time of day it also depends on the time of year, as you correctly have analyzed.

In Spring and Autumn the best time will be when the sun is near its Zenith. In summer this will be between 11am and 1pm. In general, the light is great at any time during the day, as it is the reflection of the walls that creates the beautiful colors.

You need to keep in mind that the opening overhead is not exactly above the sandy patches. The curvy walls each have their own unique optimum light position, so your calculations are not fully applicable. There are areas in the canyon that allow for direct rays well before or after the 'optimal' time of day.

Also, all the (professional) images of these canyons show spectacular colors that will only emerge with special lenses and camera positions, and it often is the excess (or lack) of light that provides these unique effects. For the naked eye the canyon is spectacular as well, but your brain will adjust the colors depending on luminosity.

The image above was shot at close to 2 pm local time (lower canyon). Other images that I took around that time still show direct sunlight on the sand.

If your are planning to go there specifically for the photography you will need to find a photographer's tour (at a significant fee) that will allow for some extra time. My guide during the (regular) tour stopped several times to create photo opportunities without other visitors in sight.

A key item that I did not find in your math: The regular tours take about one hour, but the the wait easily is another hour. So if you book the tour at noon (as I did) you will only be in the canyon at 1 pm. This was early May (2017). The wait may even be longer in high-season. See pic below. Bring sunblock and water.

Further keep in mind that there is a one hour timezone shift if you move from Utah to Arizona. Arizona does not observe daylight saving time, so make sure you include that in your math.

Rather than shooting pictures at the touristy Antelope Canyon (nevertheless an unforgettable experience) you may head for the nearby Waterhole Canyon. After getting your (inexpensive) permit from the nearby Navajo reservation HQ (Leechee Chapter) you have all day for this long and narrow canyon with similar setting and, unlike the hundreds of fellow visitors at Antelope, you'll probably see no more than a handful of other visitors, with many hours to catch the best light. Of course this will change when photography magazines start showing spectacular images of this canyon as well. Bring water and lunch and check for snakes at sunset and dawn. You can find some of my Waterhole Canyon images, including 360 degree images, on Google maps. You may also check Maps for images of the Upper Antelope Canyon to find out the most optimal time of day.

Last but not least: The Wave is a nearby spectacular area, with only few dozen visitors allowed via lottery. You may want to give that a try as well. My personal favorite, with very few pictures ever published: the off-road Cottonwood Canyon road between Kodachrome State park and Page. This 'dragon's back ridge' near Paria is unique. I can't wait to go there again. See Google Earth image below.