When someone is "on the high road to" something, it means they are making good progress and are likely to achieve their goal. There are many synonyms for this phrase that can be used to add variety to writing or speech. "On the path to success" is a common alternative, as is "making strides toward" or "heading toward triumph". "In the midst of a successful journey" works well, too. Other options include "on the verge of success," "approaching victory," or "on the track to achievement." Regardless of which synonym is chosen, all convey the sense of progress, advancement, and eventual success.