Pelz stressed a straight back and straight through stroke by virtue of a bad combination of incorrect shoulder motion and an exaggerrated vertical hinge(reverse roll of the arms!).
Proper straight back and straight through putting requires the shoulders moving around the horizontal spine, with angled hinging.
Yes, it would feel 'unnatural'. Firstly because Pelz's pils stroke is flawed. Secondly because every change you make to your previous habit will feel 'unnatural'. And if you're not convinced of a change, you won't make it.
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