How can I enlarge a doorknob bore with common tools?
With the paddle bits or the hole saw bits that you have drill a hole in a scrap piece of wood that is the correct size for the knob you are trying to install. It would be good if this scrap was at least 3/4" thick.

If you have clamps - clamp this scrap with the hole in it over the hole in the door and use it as a guide to then drill the correct size hole in the door.

You didn't hear this from me - If you don't have clamps you might be able to just hold the guide tight and drill carefully. Maybe a helper would be good. 

You could also try the sanding drums - it doesn't have to be pretty since the knob will cover things up, but they look cheap and might wear out before you get to where you need to be. 

You can do it. Go for it. Persist. Don't forget your safety glasses.