Thinking about it more, maybe I should just use "controller" to point at what I want to point at, but the issue is that is a normal English word with many more implications than I want.

Creating a new "proportioner" concept doesn't make sense to me, as there don't seem to be any leftover things to explain.

Mathematically, there definitely is. That is, consider the following descriptions of one-dimensional systems (all of which are a bit too short to be formal, but I don't feel like doing all the TeX necessary to make it formal and pretty):

1. max x s.t. x=f(u)

2. min u s.t. x≥x_min, x=f(u)

3. u=-k*e, e=x-x_ref, y=f(u,x)

The first is a maximizer that tries to get x as high as possible, the second is a lazy satisficer that tries to do as little as possible while getting x above some threshold (in general, a satisficer just cares about hitting the threshold and not effort spent), the third is a simple negative feedback controller and it behaves differently from the maximizer and from the satisficer (approaching the reference asymptotically, reducing the control effort as the disturbance decreases).

My suspicion is that typically, when people talk about satisficers, they have something closer to 3 than 2 in mind. That is...

It's just acting to reduce disturbances in current and predicted perceptions.

Agreed. But that's not what a satisficer does (in the original meaning of the term).