Not that I've ever done it, but step 0 should be to ensure that you haven't forgotten to install the little kill lever thingy. Step 1 should be to make sure the engine has been lowered into the water so you don't burn out the impeller. Then the rest of the steps you outline look pretty good except the full throttle part. What I used to do on my old Honda was prime as you described, then full choke with throttle set above the "start" setting on the grip (maybe 1/3 throttle or so). Pull a time or two and it will probably start, then, before you can get to the choke, it will die. Half to 2/3 choke the next time, without touching the throttle, and should start right away and you'll have enough time to push the choke in.
Eventually, you'll come to appreciate why we switched to an electric start. Not that it made things incredibly better, but my shoulders were happier.