Is it possible to find a model with sizeable \(c_{sb}^V\) and suppressed couplings to muons and mesons?
Yes!
Example: "Astrophobic" ALP model with 2HDM-like couplings. [L. Di Luzio, F. Mescia, E. Nardi, P. Panci and R. Ziegler. Phys.Rev.Lett. 120 (2018) 26, 261803]
$$\mathcal{X}_{q_L} = \mathrm{diag}(0,0,1)\,,$$ $$\mathcal{X}_{\ell_L} = \mathrm{diag}(0,0,-1)$$ $$\mathcal{X}_{u_R} = \sin^2 \beta \mathbb{1}$$ $$\mathcal{X}_{d_R} = \cos^2 \beta \mathbb{1}$$ $$\mathcal{X}_{e_R} = -\sin^2 \beta \mathbb{1}$$