If you have to pay Kimber and pay the shipping, then I would definitely look for a local gunsmith to do the work. You might even consider doing the work yourself, if you don't have to drill the frame its not terribly difficult.
The hard part is getting the correct replacement ejector. I don't know if Kimber is willing to sell their parts, or not, or only some of them. There are quite a few different ejectors available through the aftermarket suppliers.
Getting the right ejector is more than just getting one that kicks out the empties. It ALSO needs the clearance to eject loaded rounds.
I ran across a 1911 once that had that very problem. The owner had the gun for several months, and never realized it. He would shoot it a couple times a month, always the same way, a couple magazines, or so fired until empty. Never any problem. UNTIL one day, he tried to eject an unfired ball round, and the gun jammed. The gun would eject empties fine. It would eject loaded hollowpoints fine. It would eject RN profile snap caps, just fine. But a regular 230gr FMJ RN would wedge stuck and had to be pried out.
To my eye, having inspected hundreds of GI .45s in the army, the ejector looked wrong. It was one of the "long nose" ones (for the commander?)and not the one that belonged in a 1911. Gun went back to the maker, and they confirmed, it was the wrong one. "Don't know how it got out the door that way, but we'll find out! Sorry for the trouble,".. etc. Gun came back with the right ejector, works fine in all ways now.
so good luck with yours. Get the RIGHT part, its easily repaired. Get the wrong part, its easily installed but the problem may not be fixed.