First I'll say that this is a sure fire way to burn yourself since doing this requires either tremendous patience to do it in stages of turning it off, making an adjustment, turning it on, checking the adjustment, turning it off... Or, just leave it on and be very careful. So...
Gently pry off the cap to reveal the small screw (7mm head) which I already removed:
Next remove the nut that holds the valve in place. Oh, I guess you should now remove the lower back splash and the drip tray and also the top warming tray. NOW remove the nut:
Once the nut is off you can push the valve back. The valve is HOT so use your steam towel to hold it as you push it back.
This is the valve assembly after it's been pulled down to where you can get some wrenches on it - notice the towel I'm using to hold the steam valve:
The nut on the right (in the above photo) is the screw assembly for the valve which is the "T" part to the left. The reason there's so much slop is the the screw is a reverse thread and when it's bottomed out there's a gap between it and the valve. When you remove that "nut" you see this which looks like it would screw but it doesn't - it's the spring loaded valve and the gap between this and the reverse thread screw creates the slop as the screw "winds" down to this stud or button or whatever you'd like to call it.
So, the screw has a recess in it (center below) and the threads of the nut (brass hex in right of valve shot) bottom out before the space between valve and screw can be taken up.
In looking through all my misc screws and junk I made a happy discovery which is that the common x-acto knife handle fits this small recess in the screw perfectly. I used a dremel to cut off the end of an old x-acto handle to less than 1/8" and set it in rough edge out and then filed it smooth and flipped it over to get this - a perfect spacer.
Here's the part where you'll burn yourself if you're not careful.
With the machine on and hot you'll screw this back together but now, as you screw it together, there will come a point that the new spacer will contact the valve and turn the steam on. BE CAREFUL - you're holding the valve and working two wrenches AND (therefore) turning on the steam. If you've ever wanted to passively-aggressively burn someone now would be when you ask them to hold the valve while you screw the brass nut/cap/screw assembly back together. You'll have to sneak up to this point slowly and then install the assembly and put the knob back on and check the slop and keep fussing with it. There's a sweet spot where you've taken up all the slack but the valve isn't leaking and that should take up almost all the slop in the knob. At this point the lock screw that was pointless before this becomes useful as you'll screw that thin brass screw up against the nut to keep it in place. Once you're there "assembly is the reverse of disassembly" and, with any luck, you've got it all back together and haven't burned yourself and you've gotten rid of that annoying slack or slop in the steam knob.
Good luck!