Have you tried partial sizing? Maybe you can partial size the necks and see if this remedies the problem for the short term.
Is the brass you bought old or new? It sounds like the brass is hard/cracked in the neck area, maybe from age cracking, maybe it's not 'once fired' as you have been told.
I no longer use Winchester brass for that very reason, it is hard and tends to crack necks on the first or second firing.
I use Remington and Nosler brass only in most rifles I own.
I would scrap all of that brass, unless you know how to anneal them, and buy new Remmy or Nosler brass.
Hope this helps.