There is definitley a connection with the Alexander family in the US on the Alexander Family History web site you mention. Edward was the son of John Alexander and Hannah Smith, married at Ramsbury 22 Jan 1782. The American connection is with John Alexander, brother of Edward. If you look at my web page, at http://www.sherriff-family.comhttp://www.sherriff-family.com and find the link to John Alexander who married Agnes Buffen in 1611 at Easton Royal, near Ramsbury, you will see most of the connections that I know of, in the UK, Tasmania and USA.
The only issue I have unresolved is the bit where you say that Joseph, Matthias and John who were transported in 1831/2 were all brothers. I came across a web page with details of all the Swing Rioters who were transported to Van Diemens Land, and it is clear Joseph & Matthias are brothers, but John is shown as transported at a different time to the other two, on a different ship, and to have been born in 1804 in Pewsey. I think he may have been a cousin, rather than a brother, but I can't prove it. There was a John Noyes Alexander baptised at Pewsey in 1804.