I'm not sure if you've gone one citation deeper into the report,
Hicks et al (1985) On the Use of Monitored Air Concentrations to Infer Dry Deposition, NOAA Technical Memorandum ERLO ARLZ141 (https://repository.library.noaa.gov/view/noaa/19701)
where there's more information in Appendix C on the origin of those diagrams.
They make the argument that the turbulent and gravitational (settling) deposition fluxes are separable and additive such that the total deposition velocity is,
$$v_p = v_d + v_g = -F_p / C$$
where $F_p$ and $C$ are the particle flux and concentration, respectively. They then note that,
This simple procedure introduces a conceptual problem, however, since obviously both $v_d$ and $C$ are functions of height and $v_g$ is not.
at which point they assume two equations for $F_p$ (Eqns. C5 and C6), one for the turbulent layer and one for the canopy layer:
$$
F_p = - \left[C(z) - C(z_0)\right] \,r_a^{-1} - C(z) \, v_g\\
F_p = -C(z_0) \, r_{cp}^{-1} - C(z_0)\, v_g
$$
These can be combined to eliminate $C(z_0)$, and the result combined with the $v_p$ equation above and rearranged to yield Eq C7,
$$v_p = (r_a + r_{cp} + r_a r_{cp} v_g)^{-1} + v_g$$
The circuit diagram you show in the top right is an expression of this equation, which shows how the traditional circuit diagram can be modified to account for turbulent transfer in the presence of gravitational settling. They note, however, that,
In practice, the triple-product term in Equation (C.7) is unlikely to be of great significance unless $v_g$ is relatively large. Detailed consideration of the ramifications is not warranted, since great uncertainty surrounds the quantity $r_{cp}$ for the case of particles.
