I disagree with this "what Lash should have done" routine. If Harry was any other moral - ANY other mortal that Lasciel had seduced in the past - this would have been the knockout blow. Lasciel is presumably intelligent enough to have deduced where this trip is ending up. Running Little Chicago is possibly the least dangerous of all the things Harry is about to attempt, and it's going to get his head blown to pieces. Lash *knows* that she's not going to get anywhere with the "let me slowly guide you" routine - she NEEDS to offer him the coin. She does his best attempt, and he refuses - and by doing so, accepts that he may die by his decision. There's nothing else that she can offer.
If Harry didn't accept Lasciel when Molly was being tortured to death in Faerie, I don't see him suddenly changing his mind because everything's suddenly immediate. That would imply a decision that was only half-heartedly thought out. Harry is 100% behind his decision.
The situation you pose is if suddenly there was a battle that broke out in the middle, when the Merlin declared Molly guilty. Yet I don't see this as being any more hopeless of a situation than storming Arctus Tor, or fighting Eldest Fetch - in that they are completely hopeless, save for information that Harry doesn't have - that he has Summer Fire, or that all of Winter is away.
Lastly... I feel like you're completely forgetting about Harry's last gambit - that this is, in itself, a leap of faith. Harry places his faith in TWG, even if he isn't willing to really admit it to himself, that either he had the power to bring Molly back or that Michael was somehow involved and would appear. When every situation got grimmer - learning that the Merlin had all the votes, that his defense of Molly was over-reaching, that the Merlin pronounced Molly's death - he got more resilient and audacious.
I mean - there's absolutely NO reason AT ALL to demand that everyone must wait while the Gatekeeper makes his last vote. The chances against something suddenly changing in the few minutes it would take would be trillions to one. Yet Dresden DOES demand this, and they DO wait... not because this is the only option available to him, but because Dresden actually has faith that TWG will pull through.
To think that things might suddenly get a bit spicy, and look dire, and Lash might do her time slowy thing, and Dresden might think, "You know, screw it, this faith thing seemed like a good idea, but I might as well turn into a monster after all to rescue this kid who CERTAINLY will turn into a monster without proper guidance, which I can't provide anymore - THAT is contrary to his character. Because the more dire things look, the more certain Dresden is that those doors are going to burst open and salvation is on the other side.