Just a few suggestions, because I'd rather do this than clean out my pantry.
Note: I haven't tried these myself, but I would try them if I were in your situation (and, I'm hoping after Tom's food sensitivity results are in that we won't be in your situation).
Do you have any kind of margarine-type substitute you can use? I'm guessing not, based on those restrictions. What about mayonnaise? I know you can always make mayonnaise, and it would meet your requirements (unless you forgot to mention no eggs, just to add to the challenge). I have to admit, I've never made mayo and I know there's a trick to it. But, this is cake we're talking! It's important! Anyway, I would substitute mayo for margarine/butter in your cake frosting and go from there. If you're making chocolate icing, that should take care of any mayo taste. (You should probably refrigerate this one though, especially if you do have to make homemade mayo.)
As another suggestion (and this would add a bigger change to the taste), what about peanut butter? (Were you going to say no nuts, too
) Try replacing your margarine/butter with peanut butter and go from there. It might be a little stiffer, so you may need more milk... or maybe half PB and half mayo?
Anyway, here's a frosting to get you started (remember, I've only made the dairy-substitute versions, not the corn & soy-free version):
Alternate Cocoa Frosting
1 pound box sifted powder sugar (use your homemade powdered sugar)
3/4 cup cocoa
1/2 cup mayo or peanut butter or 1/4 cup mayo and 1/4 cup PB
1/2 cup milk substitute (or water, if you don't have a substitute)
1 t vanilla (or skip, if this is a problem)
Mix sugar and cocoa. Cream part of cocoa mixture with mayo and/or peanut butter. Blend in vanilla and part of milk substitute. Add remaining cocoa mixture and blend. Add remaining milk substitute and beat to desired consistency. Beat for at least a minute or two. Longer if desired.
Also, remember that you're adding a lot of sugar. It's going to taste good, no matter how bad it looks, so go ahead and experiment. It will be edible. (So far, my kids have not disagreed with this philosophy. They are happy to eat my sugar disasters. It's the disasters that aren't dessert-related that they stick their noses up at.)