I would not recommend vaping them directly. The slushy/icee machines, and snow cone/shave ice, flavors are syrups (sugar(s)+water) with artificial flavoring. Though the flavors very well could be similar/same as what we use to DIY; the syrup base, and all the other additives, makes it a no-go for me. Here is just one example (
from Icee's product page):
View attachment 653677
I am wondering, with all that sugar, if part of your difficulty in finding the "right" combination isn't textural? That heavy syrup creates a real thick (sticky?) mouth-feel along with a LOT of sweetness. If I were looking to try to replicate this I would be using something like TFA Sweetener at a relatively high percentage (maybe 2% to start and go up as needed), plus a Marshmallow and/or Meringue to thicken up the mouth-feel even more. That will get the texture moving in the right direction. The high percentage of sweetener will be something of a coil killer; but I think it would have the added advantage of smoothing out some of the harsh/artificial notes that often accompany the candy type fruit flavors.
Flavor is the kicker. It has been decades since I have had an Icee; so my memory is minimal at best. But, as I recall, there actually wasn't that much "berry" to it; mostly just "sweet." I don't recall either the blueberry, or the raspberry, being center-stage. They just kind of blurred together until they became nondescript. So that makes me think and equal balance in flavor/strength (though may not be in percentage due to individual concentrate strength). Finally, to give it that 'pop,' I think a lime, like TFA Key Lime or FA Lime Tahiti Cold Pressed, at just a hint, will seal the deal.
If it is too berry-ish; then I would look at cutting the berries with more subtle fruits (at low percentages) like apple, pear, or dragon fruit. This could help to dilute the berry-forwardness; while maintaining the overall "fruitiness" of the profile. This would be similar in effect to what juice companies do. Look at any major label juice like Welsh's, Ocean Spray, or Tree Top, and you will see they often use multiple fruits in a single fruit flavor label. You might see that a "Grape" juice is made with Apple, Pear, and Grape juices.
I am not really a "sweet" juice vaper but this brainstorming has me kind of curious. I may have to break out the supplies and see what I can do. I probably need to go find a slurpee first and see how bad my memory is.