The distributivity spectrum of Baker's variety

For every $n$, we evaluate the smallest $k$ such that the congruence inclusion $\alpha (\beta \circ_n \gamma ) \subseteq \alpha \beta \circ_{k} \alpha \gamma $ holds in a variety of reducts of lattices introduced by K. Baker. We also study varieties with a near-unanimity term and discuss identities dealing with reflexive and admissible relations.