We have come to a dead end here in Australia with a William Albert Matchett. He was supposedly born in 1857 but we don't know where. We have a marriage certificate dated 24th March 1879, to Matilda Doig. We have found registration numbers for 4 children here in Australia up to 1885. From them on William Albert seems to disappear. We have no death registration in NSW yet Matilda went on to have more children, with other men though it appears she did not remarry.
We have had a theory that William Albert left Matilda and moved OS.
When I read your message I began to wonder if there may be some connection. Could old William Albert have gone on to Idaho and fathered all those children you mentioned?
My mothers grandfather Robert Matchett was William Albert's son.