tl;dr Fastest Theoretical run only needs 5 Ballons.

--Edit: Done with 3 Players 1 CPU

Spreadsheet with Maths: https://docs.google.com/spreadsheets/d/1wTiimqcTWrOjnxtG4O1h-l9QAtIGyJOChLsXYJLpsq8/edit?usp=sharing

Curently I've found the fastest Route to be all Right turns. This can be done easily with 6 balloons (5S rank, 1B+ rank).

If I'm able to cut 11 seconds off my paddle time by better pathing, not bonking or collecting additional clocks. I think it could be possible to do the run with only 5 balloons (all S rank).