The height of skew Dyck paths with two variants of downsteps

Recently, in the context of walks of hexagonal circle packings, interest has emerged in the family of skew Dyck paths with two variants of down-steps. These paths have steps $U, D_g, D_b, L=D_r$. Using generating functions, the kernel method and (in)finite linear systems, contributions to the (average) height and other enumerations are made. As in many similar instances, the average height is of order $\sqrt n$. Suggestions by two reviewers are included. Third version contains some formatting