Take your time. You are right, if you are burning the wood, then slow down. Keep the cutting area clear like Doug suggested.
the other reason why you want to go slow is so that you won't burn out, or break the cutting bit.
When you are ready to sand the shape, I would recommend you mount the Dremel into the 231 table, with a fine sanding drum on it. You can slide and move the working piece around the sanding drum very easily.
If you live to love, then you'll love to live!