Yep, it's Thesaurus Talk Time. But before I list the overused word, I want to caution against replacing basic words with fancy-barely-can-pronouce words. When you replace the overused word, the sentence should flow equally as well or better. If not, you may want to rework the sentence.
to cause to move or proceed fast or faster
accelerate, bundle, fast-track, hasten, quicken, speed up, whisk
drive, goad, propel, push, race, spur, stir, urge