The fact that it is an auto-loader makes this a more interesting question. By sizing to SAAMI min you are still pushing your shoulder back 17thou. When you fire the round, the case stretches back to chamber dimensions. Doing that over and over is likely to be an issue. At minimum it will greatly reduce brass life.
Because it is an auto loader, you have to size your brass enough to ensure reliable feeding. That means not just pushing the shoulder back but also making sure you size the case far enough down toward the bottom. I would guess that 15 thou difference wouldn't make a difference in that regard, but the proof is in the pudding.
I would recommend setting your sizing die up to push the shoulder back to about 1.584 (4thou of shoulder set-back vs fired loads). Load 5 rounds like this, and shoot to see if there are cycling issues. If not, I would use this as your "spec" for future sizing. If there are feeding issues, work incrementally toward the SAAMI spec until you find the place with the least amount of sizing but 100% reliability in chambering.
The less you work the brass the better, but with an auto-loader you also have to factor in reliability and chambering. On my bolt guns, I usually bump shoulders 1thou. On my 223 auto-loaders, 4 thou I has worked for me.
Good luck with yours and let us know where you end up.
Brandon
