Nozick does not evade such examples, he bites the bullet on their consequences. Since the tracking/sensitivity conditions (the last two bullets of the OP) are fulfilled the brain in a vat (BIV) does know who won the World Series. He does know it despite not knowing that he is a brain in a vat. This is an example of what DeRose dubbed "abominable conjunctions" in Solving the Skeptical Problem:
"Accepting his treatment involves embracing the abominable conjunction that while you don't know you're not a bodiless (and handless!) BIV, still, you know you have hands."
The "abominable conjunctions" and Kripke's objections to Nozick's analysis of knowledge on semantic grounds, led even like-minded epistemologists to abandon the sensitivity conditions. But to Nozick this is a feature and not a bug. It follows from his acknowledgement of the force of radical skepticism, as e.g. in Philosophical Explanations:
"The skeptic asserts we do not know his possibilities
don't obtain, and he is right. Attempts to avoid skepticism by claiming we
do know these things are bound to fail. The skeptic's possibilities make us
uneasy because, as we deeply realize, we do not know they don't obtain; it
is not surprising that attempts to show we do know these things leave us
suspicious, strike us even as bad faith."
To an extent, this is apiece with reliabilist epistemologists, like Goldman and others, who restrict the scope of skepticism that their theories of knowledge intend to rule out. Outlandish skeptical possibilities (like envatted brains, Cartesian demons, comprehensive hallucinations, deceptive setups in pernicious Gettier cases, etc.) are simply dismissed as irrelevant. In technical terms, they are moved out of the range of "nearest" possible worlds on which the counterfactuals involved, as e.g. in the sensitivity conditions, are interpreted.
Nozick does not use this machinery, his general strategy is instead to assert non-closure of knowledge under implication: knowing p and knowing p → q does not entail knowing q. Here is his response to all examples where outlandish skeptical possibilities, denoted SK, seem to preclude knowledge but do not, from Philosophical Explanations:
"If SK were true I (still)
would believe not-SK. My belief that not-SK does not track the fact
that not-SK, so I don't actually know that not-SK. Since SK is incompatible
with p, and I realize this, how can it be that (not knowing
not-SK, still) I know that p? My belief that p does track the fact that
p, and knowledge is not closed under known logical implication.
The situation exactly parallels our earlier discussion of knowledge
and a general skepticism based (for example) upon the logical possibility
of being immersed in the tank near Alpha Centauri. The skeptic
is correct in saying we don't know particular skeptical possibilities
SK do not hold, but he is wrong in concluding from this that we
don't know anything of a particular sort, about other minds, for instance. The skeptic's alternative SK is not what actually would or
might obtain if p did not; so, we can track and therefore know p
without tracking or knowing not-SK. The dream hypothesis is similar. I can know I am not now dreaming if: if I were dreaming I
wouldn't be dreaming this. Yet I don't know I'm not dreaming this,
for if I were things would seem exactly the same. Still, though not
knowing this I now do know I am sitting before paper and writing, and so on."