For all the quibbling about what precisely an "ice free" minimum is or is not, I suspect when the switch flips it will be unmistakable. So far, "seasonally ice free" has been an incremental process - one does not have to look hard to find areas that now reliably melt out in the summer where once they did not. Rather than being locked in at the freezing point, SST's in these basins begin to rise after the ice is gone, and they cannot refreeze until that sensible heat is managed. This brings marked local changes, but to date the Arctic as a whole has been dying a death of a thousand cuts.
Arguably, there has already been a state change - rather than having an effect on only a narrow band of ice (the MIZ), waves/swells now arguably affect a large portion of Arctic sea ice. What we have now does not look or behave like the "ice pack" we learned about in elementary school. Even so, the impact of this remains complicated - things look different, but you can't really point to a large step change in the behavior of extent or volume.
I believe the real shift will occur when the refreeze, rather than working from the central ice pack out (as it has for as long as it matters), has to work from orphaned or land bound ice far from the pole back toward the center of the CAB. The most enduring cold in the Arctic (so far) has been in Greenland - unlikely to be ice free any time soon. Cold spots are also generated by jet stream waves - it is easy to imagine them being stable enough to shelter significant remnant ice. Be that as it may, and no matter how much or how little remnant sea ice survives a season, growing a healthy ice pack from the margins (across waters, exposed to sunlight and un-buffered by ice, whose temperatures are well above freezing) will be a lot tougher than it would be if even a modest bit of ice survives deep in the CAB (damping motion in the water beneath it, holding SST's at its margins firmly at freezing, from which ice can begin growing just a few degrees below zero rather than the -10C typically required in open water to overcome heat transfer from depth, and divorced from the heat of the sun almost at the stroke of the equinox). It could happen in one season or over the course of several but once the pattern of Arctic Circle in replaces Pole out, everything will be different and going back will probably not happen until long after it will matter to us, our grandchildren, or their grandchildren.
I don't expect it will be amenable to a tidy number, but as the saying goes, I think we will know it when we see it. To mis-use another cliché, we won't have to look for an "ice free" September, it will come and find us.
(Off topic, but I am afraid that even though this shift will attract attention, it won't necessarily bring about action. There are an awful lot of people out there that believe 'global warming' means they won't have to move to Arizona after all, they won't need to replace their snow blower when it wears out, Canada will become an extension of the very productive Corn Belt, and Arctic oil and minerals will finally become accessible. Going down the list of talking points - it ain't happening - if it is happening, we didn't do it - why stop it from happening because it will be great! - and finally, but never uttered in public, even supposing what we are doing right now is making the really, really bad things inevitable if they won't actually happen until long after I retire from office, who cares? Right now, we have an election to win!)