This paper addresses the critical challenge of insufficient solid-phase suction capacity in jet pumps during vacuum sand cleanout operations for low-pressure oil and gas wells. Through integrated numerical simulations validated by experimental measurements with under 15% error, a kind of nonlinear interaction mechanism among key operational and solid-phase parameters is revealed in this paper. The results demonstrate that due to intensified turbulent dissipation, particle diameters exceeding 0.5 mm will lead to a significant decrease in pump efficiency, while an increase in solid volume fraction can improve the solid transport rate but will reduce the energy conversion efficiency. Working pressure optimization shows that the pump efficiency will reach its maximum when the work pressure is 5 MPa, while if it is 8 MPa, the solid transport capacity will be increased by 116%. A discharge pressure exceeding 2.5 MPa will reduce the suction pressure difference and disrupt solid phase transport. A novel dual-metric framework considering the solid transport rate and pump efficiency is put forward in this paper, which includes limiting the particle diameter to 0.5 mm or less, maintaining a solid volume fraction below 30%, and keeping the working pressure between 5 and 8 MPa and the discharge pressure at 2.5 MPa or lower. This method can increase the sand removal efficiency to over 30% while minimizing energy loss, providing a validated theoretical basis for sustainable wellbore repair in depleted oil reservoirs.