But this is unlikely to last forever. Even if you are still in the 12% tax bracket when you start taking Social Security, you will probably be in the phase-in of Social Security taxation, which leads to a 10.2% marginal tax rate on capital gains.
Therefore, it is better to avoid using average cost, as this will average all of your shares now, and make it harder to use specific identification later, when it may matter.
The best strategy might be to use specific identification, selling the highest-basis shares with long-term gains. You could sell not only the shares you need to sell for this move, but also selling enough additional shares to use up the 0% capital-gains tax range, and buying back either the same fund or a different fund. This is known as tax gain harvesting, taking a 0% capital gain in order to avoid the potential for paying tax on that gain at a higher rate in the future.