What you might try:
About 10% of a normal powder charge of Bullseye.You might need a couple more grains,but don't get crazy!It is Bullseye.
You can use a dipper.Put primed brass in your loading block.Put the Bullseye in one case.Fill it up to the neck with Cream of Wheat(not corn meal)I use a little wad of toilet paper on top .
If you have a controlled round feed rifle,remove the bolt,install the round in the bolt,put the loaded bolt back in the rifle,and shoot it,keep the muzzle up.
If its only semi-formed,add a little more powder.I don't think I'd go past 10 gr in the 375.
If the brass is too hard,they will split.
If it works,I think you will find nice,uniform necks.
I actually took an old chunk of Mauser bbl,about 8 in long,turned it to be a bbl insert for an old junky single shot break action 12 guage,drilled/reamed the bore out to .411 or so,and ran a 40-70 Sharps Straight reamer in.
Then I use the shotgun as a fire-forming tool.