I inherited a sporterized 1909 Argentine Mauser that sadly has been rechambered to 30-06. The bore remains 7.65 or .311 as measured by slugging the barrel.

What's the most economical way to reload for this situation? I already have a Lee full length 30-06 die set for another rifle, but I'm concerned about two issues:
1. Seating the larger bullets. The neck of the Lee seating die seems to be too tight for .311 bullets (they don't slide thru). Should I hone the neck out?
2. I know that I can order a larger sizing mandrel from Lee, but will the sizing die work the neck too much (sizing it too small on the down-stroke)?

Any input appreciated. Thanks.