Let's try a different tack, since we are sailing against the prevailing winds. In 1911 Jane was one of 8 people in her family residing at 174 Alma Street, West Hartlepool and although someone has written 'Husband Away' across this page, he was hardly more than a few sheets to windward. At this very same time George was staying with John Adamson Jenkinson at 29 Acclom Street. I have found them both on an old map of Hartlepool and they are not too far apart. So was George just in from the sea and staying with a relative of Jane's because there was no room at the Inn, or were they really separated? If so then wouldn't she have got to know from John Adamson Jenkinson?
I have tracked J A J in the past to his family in Filey, but never as yet found how he got his middle name. I think that is paramount now, and you never know, finding his Adamson family may lead us to Jane's.