According to a couple of trees on Ancestry there is a Solomon, Emma, Linus and a John A. Rydén in USA that match this family with parents Anders Jönsson and Sara Stina Andersdotter.
Many of the dates of births and arrivals match all the info I have found here in Sweden.
I believe this to be the family of your Linus from Båraryd. Where the name Rydén came from is a big question.
I suppose the name was changed on the way to America. Only Linus seems to have the name Rydén in Sweden.
Ian