Hi Ralparama,
I pretty much agree with Popsbengo, consistency is key. I defo prefer FLS, as the brass is the same every time , and do use neck bushings because i can control the amount of neck expansion (and I have some neck-turn chambers). I want to use a bushing small enough, that I plastically deform the neck from the inside. So, I target the expander / mandrel moving the neck about 3-4 thou diameter.
Until recently, I also used a mandrel on the neck, to give me a nominal .002 of neck tension on the bullet. I recent bought Redding carbide button, and that seems to give same run-out....and saves me a trip through the press.
Annealing does give consistency over repeated firing of the brass. With a Wilson seating die, I can feel it, but I don't have a force gauge to actually measure it.
I do have an AMP annealer, but I used to flame anneal in a simple tube in a slow rotating drill chuck, and a MAPP gas flame. I used two temperatures of Temperlac paint to figure out how long I needed in the flame. I think it was 6 secs for the 300WSM. Clearly not as gucci, or easy to use as the AMP , but it does work.
A chum of mine has built his own induction annealer, and this is a clever way to go, if the budget it tight. Or find someone locally, who'll let you use their AMP, for a pay-per-go fee.
I do feel that with the AMP, I'm also buying a lot of know-how, as they've done a tonne or hardness testing, so their settings should be optimally effective.
Good luck on your quest for long range precisison
J