Your question implies that a stronger desire for sugar would fade along with the desire/impulse to binge, and I don’t see why that would be the case. Sugar is highly rewarding and well known to be addictive so a persistent desire is not surprising. Plus, of course, you are reinforcing by maintaining an expectation to eat particular items, at a particular frequency, in particular amounts.
Did you see the post on “The discomfort of desire” which is currently about 9 topics below this one? Worth taking a look at that.
My practical suggestion is for you to get a picture of how much sugar you’d want to aim for to be at peace. And Work Through your desire in order to get closer to that. You mention things you’ve already tried but not said why they didn’t work for you. For example, making choices in the shop – you could aim to work on buying these items less and less often as time goes by? That’s exactly what I did with pizza. You get the desire and think, “maybe tomorrow”.