WI: Successful Darien Scheme = Independent Scottish Panama?

The Darien Scheme was an interesting and disastrous episode for Scotland. It was an attempt by the Company of Scotland to colonize the Isthmus of Panama to make a trading colony between the Atlantic and Pacific. However, it was plagued with a whole slew of problems, including plague (mostly Tropical Diseases). However, others included poor planning and provisions, divided leadership, lack of trading goods, lack of English support, Panama's nightmarish geography and climate and the Spanish,

In the end, the Dairen Scheme was an absolute failure. It costed approximately 20% of all the money circulating in Scotland the failed colony left the entire Scottish Lowlands in financial ruin. This was an important factor for the Act of Union in 1707, creating Great Britain.

What if, everything went right for the Scottish? The Company of Scotland plans it out better, a large number of provisions for a healthy population, a good number of Scottish Colonists coming over, a failed Spanish response to quash this colony, and a breakthrough to the other side of the Pacific.

However, the Act of Union still happens, and Scotland and England unite to form Great Britain. But the Colony of New Caledonia becomes a hub for Jacobitism, to the point of declaring independence from England (Unless a Stuart takes the throne), forming an independent nation (Whether a republic or monarchy, that's up for debate, though republic more likely), and with support such as the French (due to New Caledonia's position on the Atlantic and Pacific).
I’m not sure there’s really any scenario in which a small band of Scots-Creoles holding a vitally important trading shortcut manage to preserve their independence from outsiders. My bet is they succumb to the Spanish, with occasional back and forth with the British, and then when/if their empire in the Americas crumbles, the British swoop in and take full control. The United States likely contests it too. The Scots in Panama then act like a sort of tropical Quebec - a misfit territory which an ethnically proud and independent population and continual friction over their status in the British Empire.
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