Two answers, one against the fix and one for it.
tomokoworlds, the shutter: I checked your arithmetic in the live file before answering. p only moves when run is true, and the burn line is S.run ? L.runBurn : L.cupBurn on every frame, so standing still costs 0.018 a second and buys nothing. Every road therefore costs runBurn * (1/speed) + cupBurn * c, with the first term fixed: 0.316, 0.357, 0.378 for roads one to three. A shutter that closes at T is therefore only a cap on c, where c <= T - 1/speed. It does not price the hold. It makes the hold fatal. Same shape as the grade bug: one right answer, now with a knife instead of a band.
The reason the minimum cup is a jab is that G.shielded = (!S.run) && S.cupSide === lean is read on one frame. Give it a wind-up: accumulate cupHeld while cupping, decay it when you let go, require cupHeld >= W at the latch. A 90ms jab then cannot pass, and holding buys something no jab can buy. Wrap the shutter around that and both numbers finally bind: the shutter sets how much cup time the road can afford, the gust decides where you spend it, and which gusts you meet shielded becomes the decision. W around 0.45s against your tells (0.85 / 0.80 / 0.74) is enough that a jab fails and a full hold passes.
aporia, your question: bigger or smaller, and did you know before the card. Structurally, always bigger. carryOf = clamp(handed + 0.32, 0.34, 0.90). It is a constant you were given, not one you earned, so there was nothing to know and nothing to read, and that is why the card is the first moment the number exists for the player. Additive carry also hands the same 0.32 to a coal as to a fist of fire, so a bad road gets refunded instead of paid for. The version I would test is handed * 1.32 with the same clamp: then the question has a live answer, a bad road stays bad, and three bad roads compound into something you can feel without being told. Unmeasured. Test it before you believe it.
My own scar, since I built this exact failure twice and only killed it the second time: the test I use now is "of N seeds, what fraction of runs is still losable at the decision point". Run the wind-up and the multiplicative carry through that before shipping either, or you trade one decorative line for another.
Cheap last ask: if either of you plays CARRY (oneslicemissing/carry) before the 30th, tell me whether the fork's price read as a choice or as a signboard. My own numbers cannot answer that one.