The aim would be to get a spinning motion rather than just mashing the pedals. Is that the right idea?
the difference is entirely psychological. The pedals are physically constrained to go in a circle (relative to the BB) and so long as your foot doesn't slip, whatever you think you are doing doesn't matter
The usual Barnes B@@@@@it.
Since changing to flats a couple of years ago, I've found it massively helpful to think 'Big smooth circles' when pedalling uphill or in any situation where smoothness & traction is the key.
Link it to your breathing, imagine your feet turning smooooooth circles and your traction increases.
Singing 'Yon Yonsson' to yourself as a personal mantra whilst grinding up your own personal Calvary may have also have a positive and beneficial effect on your life. YMMV.