I'm not from New York and have never had a Phrostie, but I assume that a big part of it is that they should be slushy? To get a product that will stay slushy (at least for a while, before it freezes hard) you want an alcohol content just around 10%, varying a bit depending upon your freezer. There is no reason that Kool-Aid and Everclear wouldn't work, but your ratios have to be right. Everclear is 95% alcohol in the 190 proof formulation. I understand that it also comes in a 151 proof formulation (75.5% alcohol), but I've never seen that.
So if you're using 95% alcohol, you'd want to use about one part of it for every 9-10 parts of mixer. Your alcohol content can be a little lower than that if the mixer is full of sugar, but not much lower or it will quickly freeze hard. If your alcohol content goes much higher than 10% (like in jsanc623's first recipe, assuming 190 proof Everclear) it will just stay liquid at home freezer temperatures.
To get the layered effect, just mix your layers with slightly less alcohol in the bottom layer color than the top. Freeze your first layer until it's good and slushy, almost frozen. Then add your more potent layer. You can freeze again to make yet another layer, just keep the total alcohol content of the bottle at just around 10%. Doing it this way, as the drink melts, it will also stay in layers (sort of) as you drink. Kind of cool (or kool), so to speak either way.
See also: What's the secret to getting restaurant-quality frozen drinks at home?, especially if Kool-aid and Everclear sounds as juvenile to you as it does to me.