I think that title is a pretty big deal - it would make Ireland the GM and perhaps keep him here longer than he would be at his current position and GM offers keep coming in.
I don't think there's any prohibition on moving Loomis to some other executive title, but where you have to be careful is where there were discretionary responsibilities to "make the call" that rested with the GM . . . as there usually are. Yes, the GM acts in service of the ownership and executive structure but that doesn't mean that the GM isn't free to make a wide range of decisions - they don't run every single thing by the ownership structure. If you were to keep that orientation in place, the GM (and those responsibilities) would become Ireland's and not Loomis's. That might not be the role Mickey wants, and he might actually be quite good at it . . .whereas Ireland is unproven. I think it's do-able as long as everyone is on the same page about it, and stays on the same page about it - but often that's just not the case.
Another thing about those executive jobs like president, or CFO, is that they typically deal with a much broader range of issue associated with the franchise - not just managing the football team. An NFL franchise has all sorts of associated contracts, leases, governmental issues, etc. that are handled by the overarching executive staff, but not within the role of the typical GM, whose job it is to manage the football team itself.