I don't know that there's any connection between the names Mingulay and Minch; Mingulay is but one of many islands reached by sailing the Minch. The Norse 'megin' theory is intriguing and maybe does after all indicate common origin for the two names for the Gaelic 'Miugulaidh' sounds something like 'Mig-oo-lye' (emphasis on first syllable and no 'n' sound; a Barra native confirmed that 'Miugulaidh' is the Gaelic name used by Barra people; I'm not sure I remember his pronunciation of the third syllable correctly; it may have been closer to 'lay' than to 'lye').
I don't know if we have more concrete evidence, but a Spanish/Portugese derivation for the Minch isn't implausible; they were seafarers.