Lag

Every time I attempt to move a token on my map, the entire game freezes. I've only ever noticed this issue on large maps, which is understandable, though I still have no idea how to deal with this.

freezing indicates a browser issue. Since the last Chrome update, freezing started for me. Try switching browsers (firefox instead of chrome) Try opening roll20 in a private tab

And clear your cache every once in a while to minimize buildup.

Are you using dynamic lighting? I have found that advanced fog of war with dynamic lighting on large maps creates a noticeable lag (with LDL, at least). If you have global illumination and advanced fog of war both enabled on a large map with dynamic lighting, you are definitely asking for trouble. Avoid this. Otherwise, it will also generally help if you try to minimize the number of DL segments in a given map, as it will reduce the number of calculations required. Not sure about the first tips if using UDL, but the last one may still help. Outright freezing is a major issue, though, so not sure how much it will help. Martijn & Cat's advice are both good.