Nice Trek 800. These are such versatile bikes. I like the idea of the 2 speed kickbacks, but never tried one. The 2-speed kickback is neat in that there are no shift cables and of course, it extends your pedaling range.
There is no rule that the front brake lever needs to go on the left side. That is up to you. And me. I used to set up my bikes with the right lever to the front brake. The rest of the world does it this way. In the United States the convention is the right is for the rear. I don't know the origin of this convention, however, I suspect it is because when adjusting the gears on a bike in a stand it is easy to stop or slow the rear wheel.
Ride it a bunch more and report on how you like it with more miles. There are probably more people interested in your thoughts on this hub. The old Bendix have been popular in the past, but since they haven't been sold in 50, no 60 years, we don't see them as much. They were considered pretty good. Sturmey Archer does indeed make a 2-speed kickback hub.
I've read that there is a big step between the low and high gear. Sort of like the jumps on Sturmey Archer wide ratio 3 speed. I haven't seen any issues with reliability of them. The coaster brakes are the plate style, so the heat path is longer for being able to get rid of the heat of stopping which could be a problem if you had a long downhill. You have the front brake which is ideal and makes this a non-issue. If you end up liking the KT kickback and go for a Sturmey Archer kickback let us know how it compares.