Vergent: I'm hardly equipped to prove or disprove your hypothesis, nor do I necessarily think that the formation of such a polar storm is unlikely, given an ice-free Arctic--but are you certain that it'll have a cooling effect? It would massively increase albedo over the Arctic, yes, but given an Arctic ocean that only becomes free of ice at the end of the melt season (the state of affairs that, one assumes, we'll hit before we hit any other more exotic states), in the polar night most of that reflectivity will go towards trapping heat within the Arctic ocean, discouraging the development of thick ice rather than encouraging it.
Now, if such a storm sprawls out as far down as 50˚ N, as you propose, and dumps immense quantities of snow on the surface...well, that would increase albedo, sure. But it would increase it during winter, when it matters least. I'm also somewhat uncertain about your statement that a polar storm is responsible for the decline into a glacial state, and that brine outflow through the Fram is enhanced during glacials (wouldn't it be reduced, given that with less summer melt there would also be less winter refreeze, and consequently lower brine rejection?). Do you know of any papers supporting those two hypotheses?
(Edit:) Another possible issue occurs to me; are you sure that the [Na+] is a proxy only for the windiness around Greenland? Sodium would also be present in dust in saltpans, deserts, etc, and of course the Earth as a whole was a drier place during the last ice age, with more extensive desertification than is the case at present. It may be that there was simply more dust in the air in general, rather than increased transport of salt spray on to the Greenland ice. I suppose one might be able to determine if that was the case by examining the ways in which the [Na+] and, say, [SiO2] varied relative to one another. If the ratio between the two changes dramatically at certain times, with far more Na+ relative to SiO2 than is the case during interglacials, that might support your position.