Solid-particle alternatives to sulfate for stratospheric aerosol injection (SAI) span a broad parameter space: particle composition and morphology, sensitivities to agglomerate microphysics, and injection strategies in latitude, altitude, and season. Spanning this space with three-dimensional chemistry--climate models is practically prohibitive. To enable such sweeps, we present a two-dimensional (2-D) zonal-mean modeling framework for SAI with solid-particle materials. ERA5-constrained stratospheric transport is coupled with explicit aerosol microphysics and a modified RRTMG radiative transfer scheme, with each component extensively validated. Focusing on silica and calcite, we use the framework to explore SAI performance across two complementary axes: material properties together with monomer and agglomerate microphysics, and injection strategies in space and time. Tropical injection maximizes radiative forcing efficacy but pays the largest in-layer heating penalty. Coagulation in the tropical confinement amplifies aggregate diameters and partially offsets the residence-time advantage. A seasonal schedule (alternating-summer-hemisphere) delivers a modest 10-20% mid-latitude gain in radiative forcing efficacy over symmetric injection, but at a comparable mid-latitude heating-cost penalty. For IR-absorbing materials such as silica, symmetric mid-latitude injection reduces stratospheric heating with limited loss of efficacy; calcite's negligible IR absorption keeps the heating penalty an order of magnitude lower across all injection strategies considered.