Recent literature has shown that the thickness of dip-coated films has a V-shaped dependence on dip-coating rate when Very stow rates are included. For supramolecular block copolymer films, small molecule (SM) uptake and film morphology are also rate-dependent, as shown previously for a poly(styrene-b-4-vinylpyridine) (PS-P4VP) block copolymer in THF solutions containing naphthol (NOH) and naphthoic acid (NCOOH). Here, these investigations are extended to p-dioxane, toluene, and CHCl3 solutions. The V-shaped thickness dependence is validated for each solvent, but with the V minimum displaced to lower dip-coating rates and thicknesses for the solvents with lower vapor pressures (p-dioxane, toluene), thereby decreasing the dip-coating rate range of the "capillarity regime" (slow side of the V) and consequently extending that of the "draining regime" (fast side of the V). The SM/VP uptake ratio varies with the nature of the solvent, particularly in the capillarity regime, where it is higher for solvents that are weak SM-VP hydrogen-bond competitors (toluene, CHCl3). The draining regime generally shows greater SM uptake than the capillarity regime, in sortie cases reaching the solution ratio, with higher uptake observed for the SM with greater hydrogen-bond strength (NCOOH > NOH). The variation in film morphology with solvent and dip-coating rate (spherical for toluene; spherical and cylindrical for p-dioxane; spherical, cylindrical, and lamellar for THF; and lamellar only for CHCl3; for a block copolymer whose equilibrium morphology in the bulk is near the cylindrical/lamellar phase boundary) depends on the initial solution state (whether micellar or not and hardness of micelles) and the SM uptake ratio. These factors, along with solvent evaporation rate and film thickness, influence the kinetics of morphology development in the drying films, the point at which the kinetics are frozen in, the effective block ratio, and the orientation of the morphological structures.