I agree it's a better idea to daisychain the power off your 300mA 9V output. Daisychain connectors are cheap.
Many digital pedals don't like sharing power so it's probably best to give each its own isolated power if you can.
However drive pedals usually don't mind - and most draw very little current, so you can run many on a single feed.
For reference purposes:
Most drive pedals are okay at 18V - exceptions being those with an internal charge pump, like klones or the Purple Plexi.
Most other pedals are not okay at 18V, especially digital ones. Nothing digital should be fed more voltage than it's spec'd for.