£1 a minute isnt too bad,I spent 2 hours doing some scroll work on a piece of walnut,wouldnt want to pay that much though!
If you ask the guy to drop the power,there will be a point where it no longer rmoves wood to the point you cant feel it.
Usually when etching wood,I set the laser weak and do multiple runs (between 3 and 4) but since your on a time/cost thing,this probably wouldnt be ideal.