"Interesting nuance I picked up talking to a number of cap folks today -- Impossible for New England to designate Danny Amendola to 6/1 cut. Patriots have to carry Amendola on their roster into the '14 league year to make him a 6/1 cut. If they can do that, his '14 base is guaranteed." - NFL Network's Albert Breer
So that ends whatever you want to call that possibility.
The debate surrounding Amendola's future revolved around something called the "June 1st designation", where the belief was teams could cut a player prior to the start of the league season, but the cap hit is applied after June 1st and spread over 2014 and 2015.
According to Breer, and upon further thought, "duh, that doesn't make sense." In order for a June 1st designation to come into play, Amendola has to be on the roster for the start of the 2014 season, or else the rules just wouldn't make sense. You can't just elect to spread money across multiple seasons if they're cut prior to the season's start.
Instead, having to hold Amendola on the roster into 2014 would force the Patriots to guarantee his 2014 salary, effectually making it impossible to save money by moving him. If Amendola is moved in any way, his cap hit will increase on the 2014 season.
So, as we should have expected, Amendola is most likely with the Patriots for another year, at the very least. Let's hope he can complete it.