If you are seeking precision handload results from your efforts this is one of those buy once, cry once situations. Redding, Forster, Wilson, and Sinclair-Brownells sell the tools benchrest and precision shooters depend on. Their carbide primer pocket uniformers are industry standards. Lapua and Starline brass when new have never been undersized in my experience. Never bought much Norma, but Rem, Win, Fed will be shallow enough that the uniformer will remove brass.
A large number of benchrest shooters used to use the Lee hand priming tool; cheap, great for feeling the seat, and reliable.
Lapua brass has a known issue with Win lg rifle primers being under-size diameter. I was about to throw away a bunch of .308win brass years ago when found this tidbit on one of the National Match boards. Other primer makes fit the Lapua brass just fine.
The Brownells tech line can be especially helpful. The techs at Redding and Forster are also excellent. A few years before they folded, Precision Shooting magazine published The Benchrest Primer. Lots of great info about precision loadiing in there if you can find a copy. Sinclair used to publish an Ibico bound book about Precision Handloading and Scope Mounting. Seen them on Ebay.
As member above says, if the .04" depth of the Forster seating ram is not enough, you are reaming your primer pockets too deep. Very easy to ruin brass if you don't know what you're doing.... Over-trimming, widening flash holes, reaming primer pockets too deep, performing some operations before the brass is once-fired... If you're looking to get the best ammunition possible, it's worth reading up on how the best shooters make theirs.
Should probably contact Forster and get their thoughts on why you're having trouble using their Co-Ax primer seater. Nice people at Forster.