Haven't found a satisfactory link to where the mun comes from - is it like the English "man" - as in Geordie speak. I've heard mynd or myned suggested by some as the origin and a Scottish mun, meaning must.
I don't know about you, but mun doesn't feel like any of those to me, although it could be one of those who knows.
How about as an idea:
On GPC, there is Myn - meaning "by" with lots of religious, sermon style links, but not sure of the feel or meaning really (or even if its pronounced min or mun, using English spellings).
1703 E. Wynne: BC 76, myn Diawl.
1803 P, myn … Myn duw … Myn fy ffydd.
1703 E. Wynne: BC 29, Myn, myn, myn, eb yr Arglwydd.
Duw and Diawl continued on into Wenglish - what about a myn, which could then have gone rogue in Wenglish.