What I ended up doing:
The base cake was Heavenly White Cake found on Allrecipes.com. I changed it by using 1/2 AP flour and 1/2 whole wheat pastry flour. I also used egg whites from a carton, rather than fresh eggs, and they didn't beat up to a meringue, but all worked out well.
Red - pureed strawberries. We went berry picking a couple of Sundays ago and I pureed about 1/2 cup to make strawberry cakes.
Orange - they said pumpkin worked well and gave a lot of flavor, but carrot was great too. I had a large can of pumpkin puree and Shara wanted the pumpkin, but it seemed like a lot for such a little batch. I bought a small jar of carrot baby food and used that. What Shara liked about the pumpkin idea was the pumpkin pie flavor, so I added a little ginger, clove, cinnamon, and nutmeg.
Yellow - took the advice to use stale turmeric - I mixed it with some water and heated it to try and dissolve the powder. It still had quite a bit of flavor/odor, so I put in a bit of almond extract.
Green - I forgot to save some of the turmeric which I had planned on mixing with the blue, so I used the India Tree colors I already had. Cheat, but not as bad as grabbing the Wilton.
Blue - Boiled purple cabbage that was in the freezer from last Fall's CSA! and mixed with some baking soda. It did turn blue but was very watery and wouldn't give any flavor to the cakes so I mashed up blueberries and added some baking soda.
Purple - Grape juice concentrate
I haven't tasted them, but they do smell good. The textures range from a little rubbery to normal cake. They look very nice though. Putting them together will be interesting. Shara wants these to be skewered, like this:
Follow-up - the kids actually payed attention to the flavors and had a fun time trying to guess what each one was. No one really liked the purple grape, but they didn't like the grape juice in the morning either. I think the favorite was the carrot with pumpkin pie spice. I also realized days after that I had used the wrong measurement for the egg whites. I thought a 1/4 cup of the pasteurized egg white = 1 egg white, but it = 1 egg. Obvious now, but at the time, not so much. I'm sure this is why they were a little rubbery. But they were also really interesting and the colors worked out better than I thought they would.