I haven't found any reason not to recommend the Fire HD10. As you say, it would be nice if the tablet matched the width of the S1 better but now that I've had some time with mine I would not pay for an iPad Pro just to scratch that itch. iPad Pros are filled with so many bells and whistles that would be completely redundant if its main use is as a companion to your S1. One advantage of the Fire HD10 is its letterbox dimensions mean less wasted vertical space on your desk, and a shorter reflective surface.
If you get the FireHD you can use this Windows app to remove all the Amazon bloatware and turn it into a minimal, friendly Android tablet:
Amazon Fire Toolbox