How to keep cream liqueur fluid despite freezing?

Lately I've been preparing small batches of an Italian cream liqueur called crema di limoncello, (in case you don't know, limoncello is a lemon liqueur made from alcohol infused with lemon zest, water, sugar and more alcohol to taste; the cream version is made by replacing water with whole milk — or, in my case, whole milk plus a bit of heavy cream — and with less alcohol). This cream is supposed to be served chilled, and because of the milk (and sometimes cream) in it, part of it tends to coagulate in the freezer, and you have to shake the bottle vigorously to mix the two parts again. If shaking is not enough, you end up having to take a thin, long stick, and stir around until it can be poured. Do you know of any method to decrease the solidification of such a product, so that it stays more fluid despite freezing? I've been reading about stabilizers, but it seems they all also function as thickeners, which I don't really need. (I'm not sure the flair is right, btw, but oh well)