Mikey, 
I haven't done any paper patching as yet.    The .311 bullets give lousy accuracy as they are undersized,    I have cast some .314 bullets and they work good at modest plinking velocities.     
The reason I was thinking about .308 and patching up is that there are a myriad of .308 bullets to choose from.   The .311 selection is a lot smaller.   
I wanted to see if anyone had some experience or knowledge with this application before I start fumbling in the dark.