This would be true if it weren't for the fact that she's described as
almost completely drained at this point, while Neji is still mostly
fresh; her poison does not seem to be fast-acting, so he might have had
enough time to run her to ground before it really kicked in... 

Sure. 
But is that any worse than fighting him now? He's only going to get more
tired, while she isn't going to get any more exhausted than she is after
that massive combo. This is a classic example of only having to fight not
to lose, not to win. 

Er... that makes no sense. She _is_ going to get more tired
after using that massive combo, probably even faster than
Neji would chasing her, since Neji is both physically fresh
and has better base endurance, and her poison impairs chakra 
control but he has to have at least enough basic taijutsu to beat
up an exhausted opponent without the gentle fist. If she fled, right
after utilizing the hidden snake hands, she doesn't really have
enough chakra left to do anything so it just takes Neji a little
longer to beat her. 

By using everything she has at once, she risks all for a chance
at victory that she will not see again. The Claw of the Fire Dragon
probably _would_ have landed too, perhaps ending the fight in
her favor, if she hadn't retracted the snakes first, thus allowing
him a moment to perform the kawarimi. 

But it probably would have charbroiled the snakes, which is not how you treat your summons.

Plus, fighting not to lose would not impress the person she
wants to impress. She wants to make it absolutely clear in Tsunade's
mind that she has become stronger, and if that means fighting to win,
then that is what she is going to do. 

I'd like to invoke The Shikimaru Rule here. Once the snakes land, Neji "loses". Because they could have been poisoned with anything. Step-and-a-half poison or whatever.

Granted, poisons like this probably don't exist in canon for plot reasons, but he's been hit with an arbitrary poison. 

Two trains of thought here.

1) Assuming sufficiently strong poison, everything after the poison lands is "overtime". Neji, in a team situation, has been disabled. So Sakura is exhibiting the Lee-like tendency to see how far she can go.

2) Not assuming sufficiently strong poison - that is, Neji can take steps to be back at full effectiveness - the best thing to do after landing the poison is preventing the target from getting help as long as possible. Meaning direct engagement, either by the ninja or by a summon.

I'm also wondering if there's strictly a reason to carry around an antidote for a poison on a summon. The risk of it being turned against you is a lot less, right?

--GF

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