Recent studies have suggested that stratospheric aerosol injection (SAI) of solid particles for climate intervention could reduce stratospheric warming compared to injection of SO2. However, interactions of microphysical processes, such as settling and coagulation of solid particles, with stratospheric dynamics have not been considered. Using a global chemistry-climate model with interactive solid particle microphysics, we show that agglomeration significantly reduces the backscatter efficiency per unit of burden compared to mono-disperse particles, partly due to faster settling of the agglomerates, but mainly due to increased forward- over backscattering with increasing agglomerate size. Compared to injection of SO2, injection of 150\,nm radius diamond particles still substantially reduces required injection rates as well as perturbation of stratospheric winds, age of air and water vapor concentrations due to the small stratospheric warming per radiative forcing. Uncertainties remain as to whether stratospheric dispersion of solid particles is feasible without formation of agglomerates.