Look to Australia for clues as to a non-slavery economy.
I'm very reluctantly with Sucrose on the economics of slavery trumping moral arguments for a good century, then it became entrenched.
Also the nature of slavery changed a lot in the 1700's from indentured servitude anyone (African or European) could be and yet earn their freedom, to lifelong bondage for Africans only needing a lot more paperwork to be manumitted.
However, I'm of the opinion that there was plenty of surplus population in the UK ripe to volunteer for indentured servitude or settlement to escape political beefs and poverty if they so chose and many did.
I wanted to point to Australia as a possibility as well as New Zealand or the Cape colony in South Africa as examples of British colonies that didn't require slavery for settlement or development.
The Caribbean element is troublesome b/c it sets the precedent of setting up plantations for cash crops worked by the cheapest labor possible with a mercantile class profiting from the inputs (slave labor) and outputs (molasses and rum). Here's a thought- say hurricanes devastate the coastal plantations
in Carolina enough that it's not seen as viable in North America?
However, a smallholder culture a la Appalachia, North Carolina, Tennessee, Kentucky, etc could very well butterfly a lot of slave-holding. Also, you mention the Quakers. Who says all the German Amish and Mennonites and other European religious nonconformists all have to come to Pennsylvania?
A lot more of them coming South would have butterflied the Scots-Irish influence that dominated Southern culture.
I'm of the opinion that Texas wouldn't have seceded ten years later b/c there was enough liberal Europeans (Germans, Czechs and others) that wanted no part of slavery to stiffen the spine of those opposed to slavery to vote it down.