Family history is generally a long term hobby so not sure about the ASAP bit !
One approach to confirm is to check if the prospective parents have left a will naming their children and giving some details. You don't seem to know a great deal about his american career - that would seem to be more readily searchable by you and may give some leads. I'm no expert in American records but sometimes I've seen that naturalization records give the date of entry - searching the manifests is a long process though many have been transcribed not all names are rendered correctly.
You can trace all the Manx Gales and see if there is a 'William' sized hole into which he might fit - there were not that many before the early 19th Century