The phrase "keeps shoulder to the wheel" means to work hard and persistently towards achieving a goal. There are many synonyms that could be used to convey a similar meaning. Some of these synonyms include "perseveres," "persistently toils," "stays committed," "remains focused," "endures," "sticks to it," "maintains effort," and "grinds away." All of these phrases convey a sense of determination and dedication despite obstacles or challenges. Using any of these synonyms can help to enliven your writing and convey a strong sense of purpose and drive. The key is to choose a synonym that fits your intended tone and meaning.