There are two holding period issues. The NUA value is fixed and determined when the shares are distributed, as is the holding period (assumed long term). Then there is another holding period. The time between your distribution and sale. That can be short term or long term, and the price change will be gain or loss, subject to its own tax treatment and put/call option strategies.
Here's an example from http://www.goodfinancialcents.com/net-unrealized-appreciation/;
Bob had 500 shares of company stock in his 401k with a basis of $10/share. He took a lump-sum distribution at retirement
in January 2006. The stock’s FMV was $20/share. Bob sold the stock in February 2007 at a FMV of $25/share. Bob recognizes ordinary income in the year of the distribution on the $10/share basis, which is $5,000. In the year of the stock sale, he then recognizes $5,000 of long-term capital gains
($20/share at distribution less the $10/share basis) and also $2,500 of long-term capital gains on the gain since the distribution ($25 FMV – $20/share at distribution). Had Bob not held the stock for one year after the distribution, the $5/share gain since distribution would have been short-term capital gains.
The NUA gain character and amount in this example does not change. The put/call interplay you mention will only relate to the post-distribution gain/loss.
Thanks again for asking at Just Answer. I'm PDtax.