Sometime ago I wrote a little bit about making this brass from .303 British on another forum.  Let me see if I can remember.  First a .308FL die with the expander ball removed, then a 7-08 die with the expander ball removed, watching the location of the shoulder you made, though that really don't matter since headspace is on the rim, it'll fireform out to your chamber if it winds up a little short to the shoulder, then into your 6x53R die.  The .308 and 7-08 sizing die bodies can be bought as parts from Lee.  I can't recall the trimming that's needed or if it would be best to do that before or after.  I do know they need the neck and shoulder annealed after forming.  Not before, you might run into a problem of collapsing shoulders.  I ran into that when I was making 6.5 Japanese from .308.  Use Imperial Sizing Die Wax and you should have no problems, even with a small press.  I was just thinking back, I posted the instructions to making that on the 1990s internet.  I was going to college then and had found a copy of Nonte's Home Guide to Cartridge Conversions in the library.  That book was so old the .308 hadn't even come about yet.  It didn't get checked out much over the years!