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Having the "Twist" there be, that for each one, Gwendolynn is half dead doesn't really makes sense to me. It's neither a condition nor a proper twist ( a twist generates a new test you have to pass)
E.g., your failure Twist on the first obstacle is really a Twist AND a Condition by having them lose supplies and get Injured/Hungry.
Also, you let the players choose whether to have a Players' Turn or not. That's really weird. Especially coupling this with your delay mechanics.
I suspect that no one will have thought to use their traits against themselves to get more checks, so they'll all have only one check anyway. That's a good chance to say "see, if you use your traits against yourself next time you'll get more checks in the player phase" and they go "a ha! I get it!"
Fictionally they might be under pressure to hurry, but that doesn't mean you need to mechanically limit them.