Mike,
There appears to have been an Old French form "Gemmes" in the mix of European forms you refer to. I suppose it is possible that this could have been favoured in Scotland before England because of the Auld Alliance.
There being no "j" in Gaelic, the usual transliteration would be Seumas (pron. "shaymus") of which the vocative is Sheumais (pron. "Haymish").
(So "Hamish" is not really a sensible formation unless you're actually speaking to the guy.)
Alan