So you try to roll low on 3d6 to succeed rolls but you can push yourself and *add* a d6 to your dice pool? This seems backwards.

That's because it is! A typo on my part that I've been meaning to fix. During a push, you would instead *subtract* 1d6 from your roll, in the hopes that you can better roll under.
Apologies for any confusion. Will try to adjust in future versions/mention this in a supplement.