Dan, I have a flex extension, similar to what you got. Mine is one of the many misc. inherited tools in my shop. I have used it only a couple times. If you are using one, the power end must be securely fastened as it wants to turn. So, the idea of a hand drill is only a 'maybe' if you can hold it down someway.
I'm thinking (I do that now and then ) that you may have hit on an idea though. If you are able to chuck your bowl to the tailstock, you could put a Jacobs chuck on the headstock, fasten the extension there and sand away on the bowl using the lathe motor for your power.
"Folks is funny critters."
Think for yourselves and let others enjoy the privilege to do so, too. ~Voltaire