I also think Kirk's scream is genuine. He has a plan, but he's still pissed at Khan.
I tend to agree with you. The Enterprise is out there - severely damaged, people have been killed, Kirk's away from the Command seat (and don't lets kid ourselves that Kirk's not in charge of the Enterprise). And for all Kirk knows Khan may look for and find the Enterprise if he acts too condident.
I'm thinking that the unbelievable aspect of Kirk's not raising shields might be because non-one can believe such as awesome Captain as Kirk could make such a mistake.
I think the 'perfect' people/Captain era started in Berman Trek so it doesn't apply here.