I really appreciate all the comments and discussion.   It is helpful to know that you think our emigrant brothers (same parents, i.e. same family) must have added the "s" to the their surname while in Ireland and quite possibly were from County Down. That has identified things a little more, even though it may be hard to trace any further, particularly since we are going back to the 1760s.

Regarding pronunciation, if I say "shoyne", it does sound very Irish. But it would seem to me that someone who heard that would have written it down as Shoen.  So I am wondering if there is another possible Ulster pronunciation for Seain (fada on the a) more like Shu-ens (as in the word "men").  We have seen Shins, Shintz, and Shinn as what was originally written down for our two brothers.

The form Shanes didn’t come directly from Mac Seáin. There were likely one or two steps between the Irish form and the Anglicised form you use today. Even if there weren’t, there’s no reason to expect the Irish pronunciation would have been particularly close to the resulting English pronunciation. Anglicisations of Irish proper nouns are notoriously crude. Many sounds in the Irish language have no direct analogs in English, and at the time that most anglicisations occurred there was no attempt to standardise English spellings of Irish words anyhow.

Thank you for your clarification.  I will set aside any concerns and just appreciate our ancestors and our name however it may have originated.