There are many synonyms for the phrase "promote too hard" that can be used in various situations. Some possible options include over-market, oversell, push too much, force, overhype, exaggerate, hard sell, and hyperbolize. These terms can all be used to describe situations where someone is trying too hard to sell a product or idea, often to the point where it becomes off-putting or annoying to others. Using these synonyms can help you communicate more effectively with others and avoid coming across as too aggressive or pushy when trying to promote something.