You may be overthinking this. When someone inherits shares, the cost basis is reset to whatever the value of the shares was on the date of death. Capital gains taxes are only owed on the difference between the cost basis and the sale price. If the death happened fairly recently, this difference is likely not very large, and so the tax will only end up being a couple percent of the overall value. Don't sweat it too much.
Also, the value of the shares on the date you receive them is irrelevant. Gifted shares retain the same cost basis that they had from when the giver acquired them.