I do have to agree with Strombeckj. While I do not use Lapua brass, (the cost is prohitive) I have used most brands of brass as well as military for my .30-06 AI. Brass prep is key, but I find that the .30-06 AI to be the easiest of all of my Ackleys to form brass.
The 6.5-06 AI is definately the hardest and the most pickey as far as brass is concerned. I use .270 Brass to form and I've used Winchester, Federal, Remington, PMC, Frontier (made by Hornady) and Hornady. I've found that case capacity is very close with Winchester, Fedral and Remington. So far the data is interchangable with these headstamps as long as the cases weigh within 10 grains of each other. But Hornady and frontier are much thicker varying up to 25g of the other head stamps. But they also are the most uniform cases. They are strong as well. I learned the hard way and lost 5 in a row. One even blew a primer, the others won't hold primers anymore. All with the same charge as the other brass. (these were full strength loads). I decided to pull them and hold the brass for working up loads specificly for that brass.
I guess what I'm saying is that Ackleys are best loaded hot, but you have to do it smartly. I used Quickload as a guide and it has helped me recognize the limits of the cartridges. Sometimes quickload was right on. Like with the .30-06 AI and 168g Bergers. I am loading safely right up to the max it lists, but with the 6.5-06 Ai its been tougher and it's the same with the .243 AI.
Hope this helps, PM me if you need help with the specifics.
Dan