It's important to lighten the chain tension before and during shifting. Once you're already mashing, that can be difficult. So, either shift sooner, or use whatever torque you can muster to put on a bit of added speed, then ease off while the momentum carries you through.

One technique that helps if the road is wide enough and there's no traffic, is to turn across the road, ie. start a slalom, then shift while there's momentarily no load. With a bit of practice this can be a very effective for shifting if you've waited too long on steep climbs.