I suspect selling is actually the best option, but that's a very rough guess.
First, the mess with capital gains won't get easier by delaying it. Why not take a rough estimate now? If the shares were gifted to you about 15 years ago, and I assume 15% long-term tax rates, I get a roughly 1/10th cost in taxes.
For the past 10 years, this stock averaged 2.7% per year, which is about +30.5% up over 10 years. But over the past 1 year the stock gained +37.3%. That tells me that for the 9 years leading up to mid-2017, the stock had a -7% loss. And that entire performance was turned around in the last 1 year. You can use your gut, and hang on until it's at a loss again. Or you can think about what "sell high, buy low" means, and realize selling now is a reasonable decision.
I'd also avoid paper stock certificates. You'll pay to have them issued, and pay to have another firm accept them. In your place, I'd sell at the high point and then buy an index fund to get the market return (and hopefully avoid +2.7% a year, but there's no guarantees).