Just to close this out, the seller agreed that it was an inferior batch of brass. Turns out he had purchased a bunch from an estate sale and this was a part of it. No telling when it was made. He promptly refunded my money.
Besides the base diameter being out of spec, the base to shoulder dimensions were all over the place. The short ones are the ones that separated, understandably.
I discovered another bag of 100 that I bought from Midway. These all checked out well and should work fine.
I would reduce your normal maximum load a bit, and seat the bullet to a solid jam in the lands. That should keep your cartridge head on the bolt face on the first firing. When you reload, bump the shoulder only 0.001" and you should be fine.