Example: instead of 2 minutes per round, let us set 10 minutes as the time limit for all 5 rounds in total. When time runs out, remaining rounds are either scored as zero, or maybe you can configure a chess-clock-style time increment.

This can make for some cool gameplay - had some fun with bullseye party games with friends doing this manually, but mostly I could see this as a cool thing for solo games or challenges, especially moving. How long do you want to spend hunting for more information, or are you confident enough in your region guess already so you can take more time on later rounds?