Another pair which might fit here is:
HENCH and FERNS
These words can be paired up to form anagrams of gifts in the song, The Twelve Days of Christmas!
(12) MR GUM + MIND-MURDERS = DRUMMERS DRUMMING
(11) PIPPIN + GRIPES = PIPERS PIPING
(10) DRAINAGE + POLLS = LORDS A-LEAPING
(9) ANGLICANS + DIED = LADIES DANCING
(8) DISLIKING + MAMA = MAIDS A-MILKING
(7) MAN SINS + WIGWAMS = SWANS A-SWIMMING
(6) ENGAGE + EASILY = GEESE A-LAYING
(5) LONG + GRIDS = GOLD RINGS
(4) DRILLING + SCABS = CALLING BIRDS
(2) ULSTER + VOTED = TURTLE DOVES
(and a) REITERATING + READ PAPER = PARTRIDGE IN A PEAR TREE
My additional pair is similar and fills the gap left above:
(3) HENCH + FERNS = FRENCH HENS!
PS Regarding the title, 'A Pairing Puzzle for Christmas':
While the 'Christmas' connection to the song at the heart of this puzzle is evident ('The Twelve Days of Christmas'), it's very pleasing that the 'pairing' nature of the puzzle is also relevant to it, since the song's lyrics focus on the gifts given within a couple, i.e. a pair of lovers ('My true love sent to me...'). This makes the puzzle's word-pairing premise a really appropriate fit for the context!