Daryl, Kennett's explanation works for your Greener 16. He states the LC, for all gauges, is only for 3" chambers or longer. (Engelhardt says it was used for 2 3/4" or longer on guns 16 gauge or smaller.) What Wirnsberger says on p. 102 matches with your Cashmore. However, later on, Wirnsberger also runs into difficulty on the gauge over C or LC mark. Look on p. 110. He has 12 over C as a 3" chamber prior to 1925, when in fact it was also used on guns with chambers shorter than 3". He also has the 12 over LC in use since 1925 for guns over 3". In fact, it was in use prior to 1925 and was dropped at that time, because the exact length of the chamber in inches was required after 1925--thus rendering the LC mark obsolete. The 12 over C remained, as a gauge marking.
Never looked at the history of those two marks before. Some interesting disagreements in the proofmark material. We probably need to get a reading from the proofhouse on those.