Cyclic polymorphism conjecture for omega-categorical model-complete cores

Let ${\mathfrak B}$ be a countable $\omega$-categorical model-complete core. A polymorphism is an operation preserving all relations of ${\mathfrak B}$, and an endomorphism is a unary polymorphism. Cyclic polymorphism conjecture. Either ${\mathfrak B}$ primitively positively interprets all finite structures with parameters, or it has a $k$-ary polymorphism $f$ and endomorphisms $e_1,e_2$ such that

$$\forall x_1,\dots,x_n.\; f(x_1,\dots,x_k)=e_1(f(e_2(x_2),\dots,e_2(x_k),e_2(x_1))).$$

This is proposed as a general tractability-related conjecture for omega-categorical cores; the source does not give a resolution status.