... and Coat of Mail prevents overwhelms against the usual double strength, but strength is no longer factored into the resolution.
but the question remains, can he be overwhelmed?
Coat of Mail does
not read, "Bearer may not be overwhelmed unless the factor being used to calculate the skirmish is tripled by the opponent", it simply says, "unless his strength is tripled".
His strength no longer matters....
I think that's our main problem here. Your argument seems to assume that
Final Triumph makes every card that references strength to be moot, and I don't think that's the case. If there were another card that said something like "While bearer is strength 6 or higher..." I think its effects would still be in play, even though the skirmish no longer relies on it for its consummation.
even though it's not a strict Cost/Effect event or ability, I still think the terminology is useful. There is a
cost of sorts....the strength must not be tripled. And if that cost is fulfilled, then the
effect is in play....bearer may not be overwhelmed. I think rewording
Coat of Mail like this would be the exact same thing:
"While a skirmishing minion's strength is less than triple bearer's, bearer may not be overwhelmed."