Makes perfect sense, Shari! Many congratulations!
So far my best triangulation effort takes me back to a colonial couple around 1700. I found four people descended from four different children of this couple who all share the same DNA segment. However my story only goes back 8 generations (my 5th great grandparents).
I also agree with your pet peeve about DNA neatly dividing. I have far too many instances in my 9 family tests where this is clearly NOT the case!