There is nothing wrong with Hornady brass.
I suggest you try different large rifle primers.
I tend to favor Federal 210M large rifle primers because I am so anal about accuracy and have measured the results with about 4 different primers and found the 210Ms shoot the best in my .308s by a very small margin.
But just about any large rifle primer will work very satisfactorily and you may find your rifle has different preferences than mine do.

If you are concerned about the Hornady brass, measure the trim length and weigh the new brass before you prime them.
It will allay some of your concerns when you find that they don't vary very much case to case as long as the brass are all from the same lot.
Different machines can churn out brass with different lengths.

The Hornady brass will last you a minimum of 12 reloads if you don't constantly flirt with high pressure and will give you a known consistent base for your reloads.
Unless you shoot over 5600 rounds a year like I do, you can reload for several years with that initial batch of brass with good success.