Throating a barrel won't help a reload that is a tad fat near the case mouth.
Kimber may have sent out a barrel with a chamber that is too tight (Under SAMMI minimum). It happened to me with an EMP. SA touched it up with a reamer and now, while it is still at bare minimum, it is no longer undersized and feeds anything that fits a Wilson case gauge. .3915 at the case head will barely fit, .392 won't. I have to gauge all my sized brass and scrap those that fail the gauge because they are slightly too large at the case head. Near the case mouth is never an issue. Too tight still IMHO, but it works.
Just a thought. May be a barrel issue.
Do sized cases fit? Obviously factory rounds fit.