Martin,
I'm a descendant of one of John Alexander's sons, Ezekiel (who migrated to Australia. I believe we have a contact in common - Janice, who is my grandmother's cousin and Janice forwarded to me the copy of the Will of which you speak about. I believe you are a descendant of John Sawers Snr. who returned to Scotland, married and had another 'legitimate' family.
I have gone as far back as James Sawers also, and have recently paid a Jamaican genealogist (Dianne Frankson-Golding who appeared on WDYTYA - Ainsley Harriot Series 5.) to research John Alexander and Jane Petgrave's maternal ancestors' origins. Unfortunately this genealogist was only too happy to take USD$400 but not provide useful information. We are now back to square one and I have found another genealogist who I think will be credible and who will be able to assist with tracing John Alexander's mother and Jane Petgrave's family. I have DOB/Parish etc. so all the information is available to begin the search.
I can send you the information I have thus far if you are interested.
I live in Australia.