@ katya_Kerensky - I am glad you like my maps and have been inspired to make your own.
You are correct in that most of my maps have used 1 inch thick foam (anything with blue foam in the progress pics is 1 inch thick). My very first map (the volcanic island with the pink foam) used foam that was just over 1/2 inch thick. Half an inch proved too thin to act as a single layer.
I live on the Texas gulf coast where it never gets that cold (we get a light snow every 5-10 years or so and some years it does not even freeze in the winter). As a result, the regular local home hardware places like Home Depot and Lowes only carry thin insulating panels, 5/8 inches thick at most.
I could have just doubled up my foam, using two sheets for each layer. That would have worked quite well from a gaming point of view, but it would have involved extra work. Instead, I bought a bulk order of 1 inch sheets from an industrial supplier that normally sells to commercial construction. They had pretty much any thickness I wanted.
But you have the opposite problem, layers that are too thick to begin with.
I do most of my cutting and shaping with hotwire tools, though I have experimented with extended "snap" blades, hacksaw blades, box cutters, kitchen knives, handsaws, and even acetone.
Every saw I have used has had the problem of making piles of electrostatically charged crumbs which are a pain to clean up. All of them also leave a rough surface to varying degrees that may not be desired in some instances.
As far as splitting the thickness of a piece of foam in half, the best tool I could envision using would be a long hotwire. I have seen rigs designed to do exactly what you need. A long heated wire is strung either horizontally or vertically and the sheet of foam moved past it. If the wire is horizontal, you can just slide the foam across a table. If the wire is vertical, you can prop the foam up against a wall or support.
I cannot think of of a way to cut very large pieces of foam sheets in half without using a hotwire. Smaller pieces of foam give you more options.
"Snap" blades at full extension are very narrow and give very clean cuts. On the downside, their thinness means that the blades have a tendency to deflect side-to-side while you are cutting. This problem seems to be more exaggerated the thicker the material to be cut is. Going slowly, using sawing motions, and paying attention to exit points as well as entry points would be key. These blades are usually no more than about 4 inches long, so you are limited to pieces no more than twice that in width or you will not be able to cut the center. If the piece is small enough that the blade will reach all the way across in a single pass, your can make sure that the blade is cutting straight by making guidelines on both sides of the piece.
The above methods also hold true for kitchen knives, though their greater thickness will make deep cuts a greater challenge taking more effort. On the plus side, their thickness means they are less likely to bend as you cut, and you can get ones in greater lengths. For splitting larger pieces of foam, I would recommend a long "bread knife" with shallow rounded serrated edges. Smooth-edged blades make smoother cuts, but are much harder to cut with whereas serrated knives aid the sawing action.
If you do not mind ending up with a rough surface, loose hacksaw blades or handsaws will let you cut through large pieces. Again, side-to-side deflection is your enemy.
If you are trying to split individual pieces in the 6 to 8 inch size closely in half if not precisely, you should be able to cut your layers with non-hotwire tools without too much aggravation. If you need to cut larger pieces, or if precision and/or cleanly cut surfaces are important to you, my only suggestion is some sort of heated wire.
I hope that helps. Good luck with your projects. I look forward to seeing your work. O0