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This work investigates the sensitivity of the cross-equatorial eddy momentum flux and its rotational and divergent components to Hadley cell strength in simple variants of the Gill problem. An expression is derived linking the divergent momentum flux to the mean meridional wavenumber weighted by the spectrum of divergent eddy kinetic energy, supporting the relation between divergence phase tilt and momentum flux suggested by a previous study. Newtonian cooling makes the divergence tilt eastward moving away from the equator as observed, but this tilt is also sensitive to the Hadley cell. As the divergence tilt is enhanced in the downstream direction of the flow, wave propagation increases along that direction when the Hadley cell strengthens. The meridional flow also plays a second, important role for cross-equatorial propagation. With no Hadley cell, inviscid Sverdrup balance requires perfect compensation between the divergent and rotational momentum fluxes at the equator. The model can only produce cross-equatorial propagation when Sverdrup balance is violated, which in the linear, nearly inviscid limit requires vorticity advection by the mean flow. As the Hadley cell attenuates the geopotential tilt imparted by the divergent forcing, the compensation by the rotational momentum flux is reduced. The linear model can reproduce reasonably well previous nonlinear results by Kraucunas and Hartmann when linearized about their zonal-mean climatologies. The sensitivity of the cross-equatorial momentum fluxes to Hadley cell strength in these solutions is dominated by changes in the divergent flux and consistent with diagnosed changes in the divergence tilt.