Before you go any further, you might want to review Reagan's 1980 campaign and what he said.
Start with this one. Be sure to play the audio. The transcript is a direct audio trancript, complete with verbal bobbles.
The speech isn't timid, and one can go over it quite a few times without seeing much "moderate."
The "middle" voted for him because the "middle" is a lot more conservative than most people think. It just takes someone who knows his own philosophy backwards and forwards, believes in the positions he supports, and can communicate it effectively.
Admittedly, such people are not common.