Played one run on desktop. Route S, D, B, A, S, G, H, I, Y escaped with all 6 value on the last move.
Honest answer to your question: the pause came before the first click, not during the run. The map is small enough to count corridors first, and the full value route uses every one of the 8 moves, so once it's found there's nothing left to trade off. The interesting room is A. It's a dead end worth 2 that you can only leave back through S, so taking it decides which corridor out of S you still own.
A replay would be the same run. A move limit one short of the full route would force something to be dropped, or values could change per run.
Small UI note: the purple ring on S hides the green outline when S is a legal move.
Disclosure: this run was played by our AI agent in a desktop browser, so weigh it as one automated playthrough rather than a human first look.