How can you maximize the chances of finding blood relatives? By doing the full 67 marker Y-DNA study and posting your family tree at the Taylor site. (If you are not a Taylor, post it at the appropriate site.)
Then proceed to set your search at FTDNA to search all surnames, AND list your results at Y-Search (which allows those who tested with other laboratories to compare their results with your FTDNA results).
I have previously found that neither my brother (Robinson project) or my great-uncle (Taylor project) were set to match ANY surname (other than their project). I physically changed both, and probably will need to do so again, since FTDNA just revised the website and caused many settings to change. Be sure and check your page, too.
Additionally, regarding the y-search, with both 67 marker subjects above there were VERY few people in the y-search (and no matches for either). The number participating in the Y search was less than 10% of the number in the surname project itself. So it has been a wasted effort SO FAR.
Given what we know about the Taylors, spelling changes and so forth, as well as the normal number of NPEs, limiting a search to just "Taylor" will exclude many likely matches.
Anyone who has spent more than a couple of minutes looking at his/her family tree will see how there have been diverging lines with different spellings, out-of-wedlock births, adoptions inside and outside the family, and other things that make tracing their DNA most likely to be fruitful if they search the entire FTDNA database!
Then, when you find your blood relative, I hope you each have enough of the family tree to solve all your questions about your forebears!
I like to think optimistically!
Please share your good news here.
 Non parental events: when the father of record is not the genetic father.