I don't know if I'd agree with 10 minutes, but maybe I was doing it wrong.

In any event, this is the way to go. The seat tube of your bike is less the a millimeter thick, so even though 0.1 mm on each side doesn't sound like much it could be significant. I was faced with the problem not long ago and found an archived thread in which St. Sheldon argued in favor of reaming but the arguments against him convinced me not to do it.