I checked the Highland Society Dictionary (Dictionarium Scoto-Celticum, 1928)
in the college library (and I see since that it is available as a gigantic PDF in
the web archive at http://www.archive.org/details/dictionariumscot10edin).
Here are some entries which might be of interest:
Bannach, adj. Actual, ipso facto, re ipsa. Llh.
Bannach, s.m. A fox: vulpes. O'R., O'B. et Llh.
Bannachd, s.f. Subtlety: astutia. O'R.
Banntair, s.m. (Bann. et Fear.), a covenanter: stipulator, contractor. Macf. V.
So it looks like Dwelly got bannach, fox from the Highland Society Dictionary,
who got it from Irish sources, O'Reilly and O'Brien, and from Llhuyd. Maybe
O'Reilly, O'Brien and Llhuyd all got it from Sanas Cormaic?
I see that the Gaelic dictionary by William Shaw, 1780, also has:
Bannach. A fox.
Could it be possible that bannach originally meant a vixen, "ban-sionnach"?