Coverage and access are different questions
Painting the whole maze creates two separate jobs: reaching every unpainted area and staying clear of approaching obstacles. A corridor that already has color may still be your only way into an unfinished branch. Before choosing a direction, distinguish the next patch you want to paint from the route needed to reach it. That prevents an attractive nearby patch from distracting you from a branch farther away.
Look for isolated leftovers
Imagine a central passage with short branches on both sides. Covering the center first can leave several small unfinished pockets that are easy to overlook. Instead of judging progress by how colorful the screen looks, inspect the ends of branches and the corners around junctions. This is a visual checking method, not a claim that any particular maze has that arrangement or requires a fixed order.
Update the plan around moving trouble
The listing says obstacles can approach, so a coverage plan should remain flexible. When an obstacle makes an intended passage awkward, retain the unfinished destination in mind while considering another approach. Avoid treating a previously painted route as automatically safe. The useful question is which unpainted island remains accessible now, rather than which direction would complete the prettiest uninterrupted stroke across the maze.
Adventure
A coverage map can make the painting objective easier to reason about without confusing painted ground with a safe route.