This is a possibility but cannot confirm for sure. Needs more research.
James s/o William and Margery Lace bpt 1781 ( 2 yrs off from your date) James is mentioned in father's 1792 will and Mother's 1813 will. Mother's will states James has 2 children James and Jane. I found no marriage recorded in IOM but there is a marriage in Liverpool in 1803 to Jane Lace. There is a bpt for James Charles in Braddan 31 Mar 1810 to James and Jane Lace no bpt for an Ann. I found no burial for Jane prior to James going to the USA.
This is speculative and fits some of your information but can't be confirmed conclusively.