Have you ever used a sextant? Introduced in 1731. In skilled hands they will get you to within one arc second of angle on the Earth's surface . . . a square that is 2.5 nautical miles on each side - a nautical mile being 6,000 feet. Certainly close enough to pick out landmarks and darned handy for sailors. Oak Island is 140 acres - or about 1/4 square mile. So a sextant would get you to within sight of the island but only about a 10% chance of being on it. Or, if you are standing on the island, you might be able to confirm you are on the proper island.
The artificial horizon is helpful but any elevation above sea level and just the crumminess of the apparatus produces even more error. And someone pretty sharp would have had to produce the star almanac for your target star. And if on the right day and at the right time you found the star wasn't quite where you needed it to be . . . do you then run around the whole island trying to resight with the earth rotating and the stars shifting from your vantage point. "Crap, missed it. Same time next year, guys?"
There's a reason GPS caught on and the US Government spent billions getting the satellites in place - it works WAY better than sextants and Bowditch.