"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."

The exersale of 800 shares constitutes disqualifying disposition and should result in a slight STCL because of transaction costs.  These should be separately identified from the existing shares he's been holding LT and sold.

Since the 800 shares sold in the disqualifying disposition are subject to regular tax already, only the remaining 1,200 shares would be subject to AMT.  It does not matter that these shares were purchased through a cashless exercise (it's the same as paying cash with after-tax money and this sum just happened to have come from a disqualifying disposition of the ISO).