On a related note, these days I am using a few White River Energetics primers for some handloads, mostly into Norma brass. As correctly stated the WRE primer cups are deeper than Federals and when seated do sit closer to flush with the face of case heads. I use a RCBS bench mounted priming tool and after the initial insertion turn the case for a second push which most of the time finally seats the primers just below the case head faces. I haven't yet needed to look at reaming any primer pockets.
Just recently I primed some
Sako 243W brass, also with WRE primers, and noted the primers seated deeper than the Norma into the pockets so for the OP if some Sako brass could be tried it might offer a solution ...?? I'm sure a member here wouldn't mind offering a couple of cases to be tried.
And, I'm not absolutely sure of this but I might also have found the WRE seating deeper in some Remington .270W brass as well. Sorry, I can't remember clearly but it may be worth trying some anyway.
Attachment 255888