I list the deepest cut at .139 according to Medeco. That is the left over blade width after the cut. It probably allows the bottom of the blade to have clearance rather than touching the shell. I think the wards hold the blade in position on a regular key, while the code setting keys sit flat on the shell. (The surface of the bore inside the shell).
You might have to sit your key a bit sideways to clear the wards.
So what you could do is cut the key to Medeco specs and try it, then just trim the peaks off a bit at a time with a file till you can get it out of your lock.
If the blade width is too small I think the keys would bend or break easily, plus they would be harder to hold while cutting. If the blade width is slightly larger (like my .150) then it just gives the pin a nice angled seat to sit on, perhaps it might set the rotation easier. I guess the root of the cut on my keys lifts the bottom of the pin just a few thou. So long as you can get it out of the lock without over setting a number six pin then the height of the peaks is OK.
With my code setting keys they don't seem to set the sidebar until you just start to remove the key. Then there is an obvious snap and the sidebar is set. This tells me pressure from the angled face of the cut is what sets the rotation. Moving them up and down and a little wiggle in and out about .030 or so seems to help too.