The top bolt on the starter looks relatively easy to remove.  I just
can't figure out how to get to the bottom one so I can remove and
replace the starter.

I've thought about pulling the starter motor apart, since it looks like
if I pulled out the smaller of the two "cylinders" that contains the
armature, brushes, etc. I would have a clear path to the bottom bolt.
Is this the best strategy?  While I am pretty confident this method
would work to remove the old one, I am concerned about whether this is
the best way to install the new one since there is a chance the
armature will pull away from the spring-loaded brushes.

What's the standard method for removing the starter and reinstalling a
new one?