One other bit of advice (which is working pretty well for me)...

Find a hill that is 'hard but not too hard' - at first for me this was just a half mile or so at 4% - do some repeats. Once that climb starts to feel easier, pick a new harder hill
(say 1 mile at 6+%)... eventually you'll get to where nothing can stand in your way.

Spending time in bigger gears on flats will help, but nothing improves your climbing like climbing.