When I shot an M-1 rifle,30-06 I used standard RCBS dies, and never needed small base sizer. I believe that RCBS makes a small base sizer though.
Have you checked your case length, and oal of loaded round? These factors could cause chambering problems. Also, do you have your dies set up correctly?
In cal 308, I used to use range pickup brass, that had been fired in Match M-14's. I reloaded this brass using a standard f.l. sizing die, and never had any chambering problems in close chambered bolt rifles. Have you checked the chamber of your FAL? It might be overly large, which could cause resizing problems.
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