You're correct, mcnor, it does wobble front-to-back but, strapped down (I use ratcheting straps), it's fairly secure. I wasn't comfortable with it at first either but, over time, it seems to work OK.
I have only jacked the bike with the trunk off (I only use the trunk when I'm on the road). I slide the jack in from the right side with the forward-most jack runner being just forward of the kickstand. I imagine that, with the trunk, the jack would have to come in more rearward and the whole thing would be a little more delicately balanced. Not sure -- that's just a guess.
When I move the "bike-on-the-jack" around in the garage, I first lower it so that the tires are close to the floor then move it gently and smoothly. That way, if it does start rocking, the tires will touch down and stabilize the bike.
Actually, the biggest crisis in confidence with that HF jack comes in lowering the bike back down -- not raising it or working on it after it's raised. That jack is notorious for working bass ackwards. But that's another story.