I have read that wine waste can help this a lot.
From chapter 9 of the Humanure Handbook:
a friend was helping me process some of my home-made wine. The process created five gallons of spent wine as a by-product. When I had my back turned, the fellow dumped the liquid down the sink drain. I found the empty bucket and asked what happened to the liquid that had been in it. "I dumped it down the sink," he said. I was speechless. Why would anyone dump five gallons of food-derived liquid down a sink drain? But I could see why. My friend considered a drain to be a waste disposal site, as do most Americans. This was compounded by the fact that he had no idea what to do with the liquid otherwise. My household effluent drains directly into a constructed wetland which consists of a graywater pond. Because anything that goes down that drain feeds a natural aquatic system, I am quite particular about what enters the system. I keep all organic material out of the system, except for the small amount that inevitably comes from dishwashing and bathing. All food scraps are composted, as are grease, fats, oils, and every other bit of organic food material our household produces (every food item compost educators tell you "not to compost" ends up down a drain or in a landfill otherwise, which is foolish; in our household, it all goes into the compost). This recycling of organic material allows for a relatively clean graywater that can be easily remediated by a constructed wetland, soilbed, or irrigation trench. The thought of dumping something down my drain simply to dispose of it just doesn't fit into my way of thinking. So I instructed my friend to pour any remaining organic liquids onto the compost pile. Which he did. I might add that this was in the middle of January when things were quite frozen, but the compost pile still absorbed the spent wine. In fact, that winter was the first one in which the active compost pile did not freeze. Apparently, the 30 gallons of liquid we doused it with kept it active enough to generate heat all winter long.
If that result were just due to increased moisture content, perhaps freezing or increased convection due to denser air removes moisture from the pile quicker in colder than in warmer weather, which would be simple to fix.
If it were due to alcohol content, then presumably other sources of alcohol would have a similar effect; you might reach out through your social network for home brewers/distillers/vinters and use their wastes. If your part of NY has wineries, perhaps the nearest one would be willing to part with a few buckets of marc.
It might even be worth pre-fermenting the most delicate of your cuttings in a loosely-covered bucket with a spoonful of sourdough starter or hooch, if you're in the mood to try a zany and completely un-tested idea. Growing sorghum as a green manure crop and fermenting bucket-length sections of stalk with yeast alone would be more certain to work, but that would be a longer-term plan.
I'm a big fan of deep mulch over and around compost piles, which you might try first if you don't do so already. When space allows, I plan to have pallets full of loose straw or similar as a compost bin. An insulating layer of browns helps the pile retain heat and moderate its moisture content, as well as drastically reducing odors.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.