Listen, I had the same problems when I first started shaving my dome. No biggie. When I first started shaving the old dome, I started out using Schick Quatro and then discovered the HeadBLade, and then the real bleeding started. I used to go to work and people would tease me, saying that I looked like I got attacked on the way to work by a blind man with a razor in each hand.
Here's what I do, some may work for you, it may not work at all: Stick the dome in the sink, get it good and soaking. Take a few drops of the scented (i.e. watered down) tea tree or olive oil and rub it in. Then take a quarter-sized portion of HeadLube or Lubriderm (with a few drops of liquid soap added into the container) and rub that into the dome. Then use the HeadBlade Sport in lines, doing the front first; then flip the HB Sport around and slowly do the back. The trick is not to apply any pressure, just drag it across the dome.
Whenver I get too many cuts, I just take a splash of hydrogen peroxide and get it gone in a second. Hydrogen peroxide will burn alright, but you'll get a beauty of a shine out of it. A few little pinprick sized cuts are nothing if you take a quarter sized portion of HB Glossy or matte finish and rub it in.