Make sure you realize that you can also pull upward on your pedals now, when you are clipped in. That means that you can use both legs for a full stroke, rather than concentrating on alternating hard pushes downward.
I find clipless especially beneficial on hills, since I can pull upward as well as push downward. Keeps my cadence a little higher to keep me moving forward!
“Hope is the thing with feathers, that perches in the soul, and sings the tune without words, and never stops at all.”
- Emily Dickinson