Well, you need 180 characters, so are there 90 good usable characters, or 60, or 45 that will work?
I’m not suggesting doing a full UTF mapping onto base64, but just 1..180 mod 3 => char base64[3] would give you 182 board positions in three URL characters.
base64 would be pretty neat! I also wonder what non-emoji unicode characters are commonly supported in paths... If say, CJK character sets were supported by most apps, single-character paths would even work.