itonewbie nailed it (as usual!)

"The 800 shares were reported on a 1099-B and included some shares that satisfied the holding period which are to be taxed as LTCG."

I guess it's mathematically possible that some of the 800 shares sold were NOT from this ISO exercise, but I've NEVER seen it done that way (and I think, if it were, we wouldn't be able to call it "cashless" anymore).  A hypothetical:

ISOs granted 3 years ago, exercised 2 years ago (not relevant how paid for) and held until today.
Different set of ISOs granted 2 years ago, exercised today.
Sold shares from 3-yr-old ISO grant with 2-yr holding period to pay for today's exercise.

But I've only seen where a piece of the current lot was sold to pay the exercise, and there's no way that would be a qualified holding period and/or LTCG.

"Presumably, these tax amounts are already reported on the W2."

I've seen this screwed up enough to never presume anything.  Get the exercise reports, get the year-end paystub and compare all of the data you have with 1) what should have happened according to tax law, and 2) what was actually reported on the W-2 and 1099-B.

Generally the Fortune 500 / large public companies get this right.  But I deal with a lot of tech companies and "beltway bandit" smaller government contractor firms and these things can go sideways in a hurry if the firm doesn't have the right team in charge of the accounting.  It can be like the blind leading the blind.

ISOs are not nearly as prevalent now (I suspect because all of the executives got hit with AMT and realized this wasn't actually saving them any taxes!) but I remember this was a huge mess back before the tech bubble burst.

Rick