Question Is there any way to control how a keyframed value changes during an Animator transition?

We have several properties that we're animating which we really don't want to blend through the transition, we'd rather than pop straight to the next value when the next animation tells them where to be. For example, a script property that swaps frames on a hand sprite. When we want to go from frame 1 to frame 4, we don't want to interpolate through 2 and 3 on the way. Changing the sorting order in layer is another one.

Within a single animation, we can get the behavior we want by messing with the tangents. But when we have an Animator transition to a new state, the blend forces curves on these that we can't seem to control.

Is this just a limitation of the tool? Or is there any way to get certain properties to pop to the new value, but still blend the ones that make sense, like position, etc?

Thanks for any insight!