The problem with those bullets is not the size (yes, you can generally shoot .310-.311 cast bullets in the Blackout), the nose profile is, specifically the "bore ride" section in front of the driving bands. You may have to seat them pretty deep.
Back when the Blackout was in it's infancy, the 155gr lube groove design was different (I have one of these), and it worked well in the Blackout. At some point Lee changed it though to be ore like the tumble lube version, with the throat interference issues that go with it. Maybe post a pic of both of yours side by side, either the bullets or the molds.
On the sizing question though - I suggest buying a .308 sizing die and polishing it out to ~.3095-.310". Those Lee dies need polishing in the taper area anyway, and it doesn't take long to open up the sizing diameter. Use emery cloth wrapped around a split steel dowel in a cordless drill.
