Bummer about your Lott . . .
I'd rather use a smaller caliber in a proven, reliable rifle than a newly repaired "thumper" that I haven't had a chance to "wring out" thoroughly.
I've used a .375 on a couple of buff and it worked just fine. (Handloaded Speer 300 AGS solids.) More importantly, no PH I've talked to has ever said the .375 was NOT adequate for buff, as long as you use either a quality solid or quality softpoint. (Winchester's "Silvertip" was specifically mentioned as a load to avoid!)
Good luck . . .