You're looking for starchy (i.e. Glucose-dominant) carbs that don't cause an insulin reaction to the glucose? I think that's unpossible, but I'd love to be corrected if someone else knows of such a mythical creature. Different carbs will spike your personal insulin different amounts, and combining carbs with fat will blunt the insulin response, but those are individual variants best determined with repeated testing with a glucose meter.
Fructose doesn't spike insulin as it is immediately shuttled to the liver. I avoid fructose, but agave syrup is known to be exceedingly high in fructose as compared to glucose...however, it seems you have the same reactions to fruit that I do, and perhaps you would be best served avoiding high-fructose foods as well. Um...sugar? It's 50/50 and that seems to work for a few out there.
I'd experiment with all colors of potato, tapioca, rice, cassava and meal combos to see if you can find a few combos that don't spike your insulin out of range; they're all going to cause some sort of insulin reaction, though, since that's what your body should do in response to glucose-