I'm dabbling in making fake moonshine, e.g. flavored spirits. I made an apple pie moonshine with apple juice, spices, and everclear, but no fresh fruit. My next project is a cranberry moonshine. I'm thinking I'd like to use vodka instead of everclear for less bite, but I'm assuming the alcohol helps make the drink shelf stable. Do you think vodka is still a high enough proof that it will be or should I stick with the everclear?

Can't help you on the shelf stable question, but Everclear is essentially just an extremely high proof corn vodka. Switching to a wheat, rye, or potato vodka might mess with the flavor.

There are some corn vodkas out there, I think Rain is one, made at the Buffalo Trace distillery in Kentucky.

But the flip side is that a corn vodka is just watered down everclear, so you could accomplish the same goal by simply diluting your everclear with purified water, until it's at a palatable strength for your tastes.

Unless everclear has changed since my college days a 50/50 mix of everclear and water should yield an approx. 100 proof corn liquor.

35 parts everclear to 20 parts of 80 proof vodka will yield a 150 proof spirit. That will get the alcohol down to make it more palatable.
If you're worried about shelf stable, strain out the fruit and store the vodka in the fridge or freezer.