Nino, you have only one mutation at 34 markers and according to your family tradition your common ancestor born around 1550!
It's great!
Unfortunately you have non-standard set of common markers (not 25 or 37). I don't know average mutation rate per generation per marker for your 34-marker set. Therefore, my estimates are very-very approximate, moreover that the calculation of TMRCA on the basis of only two haplotypes are incorrect. And yet, I will risk.
I'll take the average mutation rate per generation for FTDNA-standard 25-marker haplotype - 0.00184 per marker.
You have 1 mutation at 68 (34 plus 34) common markers:
1/68/0.00184=8 generations! It appears that your common ancestor could lived later than in 16th-17th centuries. Your common ancestor could lived in the 18th century!
Nino, I do not insist on anything. This is only my opinion, only my comment and it may be mistaken.
I would like to hear the opinion of our experts, especially the view of Vadim Urasin (wertner).