I've done a great deal of research on Leverett, which I won't go into again since I wrote about it here. I've also done research on his mother (here and here), but cannot find his father, whom I have multiple names for.
So, I decided to see about getting help researching this family. I posted my problem family on Ancestry.com's expert connect and was able to hire a professional genealogist to help me. She's going to evaluate my research and then build off of it. To start with, I've purchased two hours of research and can add more if things look promising. She'll be doing the research today and I should hear back from her in about a week.
Hopefully soon, this family won't be a brick wall - or at least this generation won't be!