When I get a hold of LC 308 brass I do the following.
Tumble the hell out of it. It's dirtier inside, than you think.
Anneal it prior to re-sizing.
Lube the hell out of it, especially inside the case neck.
Ensure your dies are clean inside, no grit, old lube. I use brake cleaner and scrub it clean after disassembly.
I've never used a small based sizing die. I reload for M1A, and have never needed to use one.
LC brass is thicker, resulting in smaller case capacity, work up loads accordingly.
I have had to run the ram twice, back to back, to get the case to resize and fit into a gauge.
I use a 45 degree chamfer tool in my dewalt drill to remove primer pocket crimp.