I'm going to make this a separate post, instead of adding to the one above.
Upon reflection, we sorta did something similar, though it wasn't our intent initially. We sold two equity-rich houses and paid a shit-ton of cash for our current home. Five years later, mortgage rates are still low, and we occasionally wish we had grabbed some fistfulls of that cheap, tax-favored money.
Our consolation is that housing in the Bay Area has skyrocketed in the same period. We kinda overpaid for this house (bidding war), but it has increased nearly 50% in value, based on recent comps. It also serves our specific needs at this point in our lives. Equally important, our big pile of other assets has grown quite nicely, too. We, like you, are not dependent on the equity in our home to achieve FI/RE.
With the info you've provided, it's probably a coin toss, but you can still sell the shares if you wish and wait to decide about paying off the house.