It doesn't seem necessary to use a tapered roller bearing for this application. You are already supporting the shaft with the pillow blocks to eliminate the angular misalignment of the shaft, so you really just need to support the axial thrust of the shaft. A thrust ball bearing will work fine for this, and be simpler and cheaper.
A)The tapered roller bearing is not being used for misalignment, it's for thrust only and will last for years.
Also, if you use the tapered roller, you may have to worry about the shaft actually lifting up from the radial forces of the pulley. (Not likely from the stepper, but still a potential problem.)
A)the weight of the antenna and the pillow block set lock screws will prevent any torsional stresses from lifting the antenna.
I agree that the Tapered Roller will work fine for a long time. I am merely pointing out that it is probably overkill, and IMO not necessary.
Tapered rollers, when used in opposing pairs, are great at resolving multi-directional forces. Eg: Bearings placed with opposing tapers at either end of the shaft will keep the shaft aligned in all directions, because of their ability to resist both thrust and radial forces. Of course this setup requires some method of pre-loading the bearings, thereby making the setup slightly more complex.
In the OP's scenario, using a steel ball or needle thrust bearing will resolve any forces at play, be somewhat simpler to implement, all while saving a few bucks.
The point about lifting the shaft is, as I mentioned, unlikely. But I felt it was worth mentioning while on the topic of bearing design.
-Cody