"The cost basis for us is zero since this was simply awarded and we'll pay tax on the entire proceeds, correct?"
It's impossible for anyone here to answer that particular question "definitively." Employers are not really allowed to make non-taxable "gifts" to employees, except in very nominal, minor amounts. You can understand why that's so: if employers could make "gifts" of stock to employees then the employer could avoid paying payroll taxes on the "gift", employees could avoid having taxes withheld from these "gifts", and so forth. So most grants of stock, stock that the employee could sell the day they acquired it, is considered "compensation" and that compensation shows up in the W-2, and the employee and employer pays taxes on that compensation.
"Final question: How is this coded in TurboTax? The drop-down box had options such as ESPP, NQSO, RSU, etc., but this was none of those; it was simply awarded. What is the correct acquisition designation? "
The correct acquisition designation is that you "purchased" the stock on the date you acquired it and purchased the stock at the same per share "fair market value' the employer used to calculate the compensation reported on the W-2, if any.
That's not to say that every grant of stock shows up on the W-2. I'm sure that employers, either through ignorance or guile, omit that on the W-2 meaning that "in effect" the stock was a "gift", though that introduces another wrinkle: recipients of "gifts" inherit the basis of the grantor of the gift.
The "most correct" answer to your question is: go back and look at the W-2s for the year of the grant to see if the stock is included in that year's W-2. If it is then the basis of the gross number of shares in the grant, before any shares were withheld or sold "for taxes", is the same as that compensation. Nobody here can look at that information and make a determination. Only you can. (Of course if your income is such that the LTCG is taxes a 0%, then there's no point in even determining a correct basis. You taxes will be the same with or without a basis figure included in the sale.)
