Okay, I'm autoreplying to... myself. Nevermind.
Until some kind of clean solution appears, it turns out that the only way to reach my goal (amongst other things, properly pause an animation clip) is to use a ... blendtree.
One blendtree, two motions. First has a speed of 1, the basic by default value.
The other has a speed of -1.
Then in the blend value of the blendtree, you put
0.5.
It shows as a float (which you can rename) in the Animator's Parameters' tab.
And
Set Animator Float is the action that will let you change it.
No comment.