Let me begin by saying that I've only glanced the companion paper very briefly and, although I have noticed the paragraph you quote, I may be unaware of other parts that directly address my response.

My remark that the approach wouldn't work in a Stern-Gerlach experiment was aimed at the three steps structure of the experiment, not at the decoherence happening. If we consider the Stern-Gerlach apparatus as the observer, sure it decoheres, but there's no middle environment upon which to distribute the measure of the system observed.

To make Carroll-Sebens procedure to work, you need both a three steps experiment and a wide middle enviroment, so it won't work in any case where one of the element is missing.