You might want to dilute it by adding a lot of other materials to it. If all you are adding is kitchen scraps, you need some browns anyway. Without browns the kitchen scraps may get smelly from too much nitrogen. The high pH will exacerbate this by driving off ammonia. Mix in dry leaves or other vegetation, shredded paper, sawdust or wood chips. Eventually it should balance out. If you have a lawn, and your soil isn't alkaline already, you can spread a lot of ashes on a lawn and still have a very thin layer. Just sayin'.

If you have finished compost now the time to spread it on your soil is now. There is no good reason to wait until spring to spread the compost you have now. Compost can be spread on soil anytime it is ready, finished, although few of us would do that when the garden has 4 feet of snow on it.

You are on the right track with straw or paper. Cardboard (paper towel and toilet paper rolls, corrugated, etc.) work well. Save some of those fall leaves in bags or a chicken wire bin and layer them with food waste throughout the year. Shredded yard waste, wood chips, sawdust all work too. Grass clippings are high in N and although they make good compost, they too need browns added just like kitchen scraps. But even if you don't compost the grass clippings, the lawn crew should be returning those to the lawn using a mulching mower, or just left them fly out the chute. That sandy soil needs all the help it can get, and bagging and hauling off the clippings is like strip mining your nutrients off. It will be less work for them anyway if they don't have to bag. Good luck and keep us posted on your progress.

+1 with the top layer of leaves. I do my pile in layers, using a water can to wet each layer as I build it. I will admit it takes a knack to build it that way but I can get it hot in a day or 2. I don't turn my piles either. Once the pile is hot I make a hole in the center for any new kitchen scraps, again covering over the top with leaves. While the pile is cooking I need to add water almost daily. This may not be the best way as it doesn't cook all the weed seeds on the perimeter of the pile, so I try to put anything with seeds in the hot center of the pile. Once it begins to cool down I may turn the stuff from the outside in but then I may not. Depends on me and/or the weather. Now for the reason - the reason I don't mix it all up in the beginning - besides being a lot of work is that mixing up so there are kitchen scraps scattered thruout the pile not only attracts rodents but insects which can be hard to get rid of. As mentioned covering the top with a layer of leaves keeps the insects away. I do have one bin made from hardware cloth that will exclude any rodents but I find it impossible to exclude insects. Also you should have a way to cover a pile when it rains or that can slow it down or stop it completely. A tarp or an old shower curtain will work just make sure you have something to hold it in place.