Hi, Mark. Generally speaking, a genetic distance of zero at 111 STR markers means a 50% chance that two men share a common ancestor within two generations; a 90% chance within four generations; 95% within five; and 99% within six. You've got the correct line.
The "TiP" tool at Family Tree DNA will help narrow those probabilities a bit, but it's still all about probabilities. From your display of yDNA matches in your FTDNA dashboard, next to this match's name click the little "TiP" icon. When it displays, set the the option to display the results for each generation, not every four. TiP tries to take into account the variable average mutation rates of certain markers--and in some cases, mutation rates within specific haplogroups--to refine the odds. I believe they'll still show it's a done deal by or before six generations, but may refine things a bit for generations three to five.
From the info, since the MRCA would seem to be, at most, Jeremiah Leak's father, this puts things within the generational range for autosomal DNA detection.
With the current sale at FTDNA, a $59 Family Finder test on your new cousin's part should help nail down the relationship; you can transfer your Ancestry raw data to FTDNA and pay a $19 fee to "unlock" it for matching purposes. The results would clarify one of three possibilities: you and he share around 215cM, are 2nd cousins, and both descend from the same son of Jeremiah; you and he share around 55cM, are 3rd cousins, and descend from two different sons of Jeremiah; you and he share around 15cM, are 4th cousins, placing the MRCA at the generation of Jeremiah's father, meaning that it's likely one of Jeremiah's brothers is actually the 2g-grandfather. I sincerely doubt the MRCA is any farther back than Jeremiah's father.
The DNA can't tell you precisely who Haney was interested in, but you've already narrowed it down to the neighborhood and another step with autosomal testing should rule out most of the houses on the block, letting you focus your paper-trail research on very specific targets.
And I agree with Laurie: you can/should add the Leak families to WikiTree, or expand the details/source citations if they're already present. Gives you a place to organize your research; let's others in the same related lines find it; and your new cousin may want to join and help with the documentation. I personally wouldn't flag any of the four brothers as even "uncertain" as your great-grandfather at this point; you have strong evidence that you have the correct family, but it sounds like you're still a bit too far away from forming a workable hypothesis about the specific individual.
Good luck! You're close to big breakthrough!
