Starline brass
I too was having difficulty locating Starline brass.....solved that conundrum by calling Starline....finding out when their next batch of 357, 44 spl and 45 LC brass was going to be run.....placed an order with the nice lady over the phone....and when they ran the next batch of each, they charged me for it and shipped it...problem solved.
In regards to the issues you are having with the Winchester brass....w/o sitting at your bench and trying to load your brass on your setup....I am as puzzled as you are....I have been loading WW 357 brass since the 70's and have loaded a couple hundred thousand rds of 357 since I started....almost all of those loads ignited with CCI primers...never had any chronic problems with seating primers.....as far as the flaring/charging die...as long as I keep case mouths lubed ( I lube every 3rd or 4th if I am loading with a progressive - I lube them all if I am loading w/ single stage) I have no issues.
I have loaded thousands of rounds during the past several decades with Winchester brass in various calibers and it has always been my " go to" brass....the reason I started using Starline was that I simply could not find any WW brass for what I was wanting to load a year or so ago....so I started buying Starline direct from the factory and have been using their brass since then, but I still load what WW brass I have w/o issue. Wish I could be more helpful for the OP, but this is like trying to trouble shoot a mechanical problem over the phone....when I need to see, hear and feel what is occurring.