What if Toussaint Louverture had switched his allegiance from the French to the British during the Haitian Revolution?

My (optimistic) idea is that, after he joined forces with the British against both the French and Spanish, Toussaint would have helped secure a British foothold on the island. He would have won a guarantee for the abolition of slavery and the slave trade from the British, and maybe the British would have kept their word, extending abolition of both throughout the British Empire over the next two-three decades. In all likelihood, however, political enfranchisement of the majority-black populace would have taken much longer.

The furthest that people of color got in enfranchisement at any point in the 19th century was Dominica’s legislative assembly from 1835, when the first three men of African descent were elected, to 1896, when the by-this-time-half-elected-half-appointed assembly was abolished in favor of directly-controlled crown colony status. Throughout the British Caribbean, even after slavery was abolished, the British maintained a racial caste system which favored a minority of white planters against the black and mixed-race majority.

I fear that a Haiti which was autonomous from Britain would not have been too different from these other British colonies, beyond the most crucial gains of the colony’s violent separation from French rule. Questions remain:

• Would Toussaint and his generals have helped lead this autonomous polity as viceroys?
• What would Britain have brought to Haiti which 1) was common in other colonies like Jamaica and 2) was not endemic to former French colonies like Haiti?
• What about Westminster-style parliamentary government? Would Haiti have adopted this instead of the big-man presidential system of the United States? And who would have been allowed to participate at the time, or would they have also been allowed to participate by the 20th century?
• Whither Spanish Saint-Domingue? Would the Spanish side have been taken over by the forces of Toussaint et al? And if so, how would that have unified the island?
• Would the Westminster system and other British mores, unified by the abolition of slavery, have helped the citizens of this island and their political system up to the present?
• How would a British Haiti have impacted Simon Bolivar and his independence movement?
• What impact would this have on African-Americans? Or on Afro-Caribbeans?
• What impact would this have on the Louisiana Purchase?

I think this is worth looking into.