When it comes to describing movement, there are many synonyms that can be used instead of "moving across". Some options might include words like traversing, journeying, crossing, wandering, or meandering. These words all connote some sense of travel or exploration, and they can be used in a variety of contexts. For instance, someone might traverse a mountain range or journey across the country. Meanwhile, someone else might meander through a forest or cross a river to reach their destination. By using diverse vocabulary and experimenting with different synonyms, it's possible to add more nuance and flavor to writing about movement and travel.