Putting in extra effort on a climb may bag you 2mph increase, but the same effort expended on the flat would increase your speed by maybe 5mph.
On a long ride you shouldnt blow your energy on a big climb, but spin steadily and efficiently to conserve energy.
Are you riding with a triple chainset or a racing double chainset? What is your lowest gear?
I ride some very steep short hills and some evenings, ride intervals up the steepest one. I managed to do the climb 5 times in a row once. Im a wreck by the time I reach the top, but recover on the roll down. That is about the limit of any training I do, and its really for fun rather than to "perform" better.