I think the Triangle has yet to see a "true" extremely big dog in December even looking back into the mid-late 19th century, and the 9.1" single-storm record is the most likely single-storm monthly record to fall someday imo esp when you look at the December snowfall records in nearby locations. If the I-95 corridor and southern coastal plain can see 15"+ there's no reason to believe something similar (even in a slightly warmer climate) can't happen in December over RDU.
View attachment 6583
December 1896, 1917, 1930, 2000, & 2002 are a few other notable close calls where RDU could have easily topped the record if everything fell into place just right.