A yDNA is not necessarily a Magic Bullet, but with work it can provide avenues of research.
I would suggest that you buy either a 67 or 111 yDNA test, then if you get the results you seek fine, the main usage of a Big y test would be in providing a more accurate haplogroup.
I did a y111 test and the results gave me matches with the closest match predicting that we have a MRCA from about 1750.
The second closest match has a predicted MRCA further away in time.
Both these matches have the same family surname and this confirms to me where the NPE in my timeline is likely to have taken place, namely 1880.
One thing to note is that you may not find the actual “Family Surname” that you seek, you will more likely get hundreds of matches with hundreds of different surnames.
I got lucky in that the results above confirmed my research into a particular family.
The link is to a pretty good tutorial, there are two in the series.
https://www.youtube.com/watch?v=67P9hv7nDZg