You should have received a 1099-R for the disbursement so presumably you've already reported that.

"My understanding is that the cost basis was reset when I moved them, and that I have should leave them there for at least one year to be able to qualify for long-term capital gains taxation."

Your understanding is not exactly correct.  Typically the 1099-R in this situation will have 3 boxes filled in, Box 1, Box 2a and Box 6 which is the difference between Box 1 and Box 2a.  You get taxed on the Box 2a amount and that's the basis of the stock. 

The NUA is "long term" by definition.  You could sell the stock the same day you received it and get LTCG treatment.  If the price changes from the price at distribution then the "differential" in the price is long term or short term gain or loss depending on how long after the distribution the distribution you sell.

Tom Young