I used to employ a similar strategy of sprinting into climbs and down shifting as I slowed. It never seemed to be effective except on small hills. I'm a few weeks into standing up on the pedals and climbing in a middle gear, putting a lot of my weight on the handle bars and letting gravity bring me down on the pedals. It is a bit more vigorous and strenuous but also much much faster. So while I'm totally exhausted and eventually have to sit down on bigger hills I am reducing the climb duration by a large margin. The big hill on my ride used to be 12 minutes on the granny gear is now 7-8 minutes with a lot of ground covered by standing before I settle down to the granny gear 4-5 mph pace. Food for thought for you.