Letting the brass sit in the die when sized for three seconds is a good idea. Annealing prior to sizing is protocol.
The big obstacle to overcome on machine gun brass is the expansion at the web. When the round sits in a hot barrel, pressure on that round is HOT, thus expanding the web more. You have to be aware of this issue and cull that brass out. The first time you seat primers in your "new to you" LC brass, if the webs have been expanded, the primers will seat a lot easier. So, cull the brass with easier seating primers.
With the LC brass that I am shooting, the barrels are Krieger and Brux with custom Palma short freebore chambers for use with 155-169g MK and 175g TMK. Accuracy is fantastic with case culling and prep.
No doubt, it is a labor of love sorting/culling brass with case prep....pass the Lapua, please.
When I form the LC brass into 6 XC, turn necks, square pockets, and de-burr inside flash holes, accuracy is superb, to say the least. This is a labor of love in a Winter project, but the payoff is great.
We used to be able to get 1000 new Lake City for $159 per thousand, then it became $159 for 500, and now it is not available at any price. I have had great service out of once-fired PMC brass, but the use of a small base sizer is required.
Brass spring back is real, simple physics. For guys that shoot range pick-up brass, the issue of Brass spring back becomes a real issue for a custom chamber. Factory chambers have liberal dimensions, hence spring back will be less noticeable if at all. The same would apply to brass that has been fired in a Rem semi-auto or Browning semi-auto.
It is prudent to use Lapua for serious target work, and I have plenty. 5 years ago, I bought a bunch of once-fired Lapua that had been shot in Match rifles of some kind. I ran into the same problems, brass fired in different chamber issues with web expansion variations, which meant that my purchase was "penny wise, and a pound foolish."