This research addresses the challenges of heat transfer optimization in non-Newtonian Boger dusty nanofluid flow across a stretching sheet by investigating the combined effects of viscoelasticity, reversible reactions, magnetohydrodynamics, and buoyancy forces. This study is highly relevant to various engineering problems, particularly in solar energy systems. In such applications, stretched sheet models simulate solar absorber surfaces; dusty nanofluids enhance thermal absorption and conductivity; nanoparticle aggregation affects thermal efficiency and flow stability under solar exposure; and magnetic fields regulate the fluid motion in magnetized environments. The effective thermophysical properties of nanofluids, incorporating aggregation and homogeneous models, are analyzed using the Tiwari-Das model. The non-dimensionalization of the governing partial differential equations is carried out via the similarity technique, and the transformed ordinary differential equations are solved using the shooting method and the Runge-Kutta-Fehlberg (RKF45) technique. The consistency of numerical results is verified through comparison with previously published research for limiting cases. The influence of underlying factors on flow and thermal characteristics is systematically explored through plots. It is observed that aggregated nanoparticles constrict streamlines, diminishing flow speed while improving heat transfer by augmenting temperature and Nusselt number. Dusty nanofluid moves more slowly than pure nanofluid due to higher drag induced by suspended dust particles. The equilibrium constant positively impacts the temperature profile, whereas the velocity and concentration profiles are negatively affected.