Yes, group 7 at the Hawkins DNA site was the group that I thought our Hawkins Y-DNA would fit into. I had studied them all, and it was mostly the photographs that convinced me this was my line. Instead through the Y-DNA our line is matching closely with some Gibbs submitters. Now through the Family Finder Test which males and females alike can take, I have over 100 cousin matches to many of my lines. You then have to work on those matches and discover how you connect. The FF Test does give you an approximate generational distance from your match and you can contact your matches and try to solve the relationship and hopefully grow your tree, fill in the missing links, hear a story or two, and if you are lucky find an old photograph! With the cooperation of several of my matches we have discovered some of our common connections.
Recently I have had a discovery of a connection and I am after all related to your family group 7 with my Hawkins after all. In looking at every scenario, and discussions with several researchers, and since I am a Hawkins with a Family Finder DNA connection to this Hawkins group, the assumption is a false paternity. A Hawkins girl from Family Group 7 must have had a child, by most likely a Gibbs man, and her son carried her Hawkins name down, perhaps her parents raised their grandson as their son, or perhaps it was due to the Revo War and was a rape by invaders, which was a common occurance. We believe this was pretty recent. I did find some Gibbs on the 1830 Henry Co., TN census in the close proximity of my line. They are unaccounted for Gibbs at the Gibbs DNA project.
You can upgrade your Y-DNA test to a Family Finder without submitting a scraping again through FTDNA. I hope those in this Family Group 7 at the Hawkins Project will consider testing at this level. FF shows about 5, possibly 6 generations back, but there are 3rd party sites which I am involved with that are going much further back. My connection to your Philemon Hawkins line did not show until I tested my (Hawkins)aunt which is one generation removed from my test.
I should have your email addy somewhere, mine is firstname.lastname@example.org