How do I encourage funnel cake cohesion? I tried making funnel cakes this weekend.

The recipes I looked at were all very similar, basically pancake batter that is deep fried. I used this recipe: http://www.foodnetwork.com/recipes/paula-deen/funnel-cakes-recipe-1947494

Instead of AP flour I used whole wheat.

I expected that the stream of batter would fry into a mass of crispy snakes as I recognize a funnel cake to be. Instead, when the batter was drizzled into the oil, it fractured into a million tiny drips. The result was more like crispy rice than funnel cake. 

I tried cooler oil at 300F and hotter oil at 365F. I tried drizzling through thicker or thinner orifices. I tried letting it stream longer and shorter (more and less batter). In every case the result was the same. The batter practically exploded.

I realize that whole wheat flour has more fiber and less available protein than AP. In other recipes, I've only ever had that make minor differences in texture.

Was the flour substitution enough to precipitate this calamity or is there some other factor I should consider?

I will try again someday. At the moment I'm kind of put off the whole experiment.
The whole wheat may be your issue. Try adding at least half AP flour or bread flour, which are both better at forming glutinous strands that will keep everything sticking together. If you want to stick to 100% whole wheat flour you could try adding an extra egg to help bing everything together.