Yes, the use of family names is a nice confidence booster.
Other things - like the locksmith occupation are also positive associations.
I really feel it is the correct family too. It is a shame that records are so patchy, however at least there are some that you can use to sketch out a tree.
The other day, I did spend many hours (most of the day) looking at this Brewood family, and there really seems to be only one main Willetts family connected to Brewood in the relevant time period.
There is another lot of Willetts who are a long way off in Staffordshire, in Rowley Regis - way on the southern side of Wolverhampton. They are a very different Willetts group, and not connected to the Brewood lot, although may have the same roots much further back in history.
If you have taken a DNA test, you might look for a link with the descendants of John and James Willetts who remained in Brewood / Wolverhampton area. That is about the only way you would know for certain that you have found the correct family.