Option 1 is a better choice.
If the manual pump is functioning correctly, no check valve will be needed and the electric pump outflow will be fine.
I'm curious about the 3/4" to 1 1/8" transition in the MP intake line. That seems unusual and would cause some restriction and decrease in the pumps capacity. If this is how his manual pump is current set up, this may be the cause of its poor performance. 1" of water in the ¾" section of how is only ⅔" of inch of water in the 1 ⅛" section. That means the pump has to work harder to pull water into the hose and discharge it. Going from small diameter to larger diameter on the discharge line is better than small to large on the suction side.
Before going to the expense and work of adding an electric pump, increase the size of the manual pump intake line to the designed size from the pump manufacturer, probably much larger than ¾".
If the manual pump is functioning correctly, no check valve will be needed and the electric pump outflow will be fine.
I'm curious about the 3/4" to 1 1/8" transition in the MP intake line. That seems unusual and would cause some restriction and decrease in the pumps capacity. If this is how his manual pump is current set up, this may be the cause of its poor performance. 1" of water in the ¾" section of how is only ⅔" of inch of water in the 1 ⅛" section. That means the pump has to work harder to pull water into the hose and discharge it. Going from small diameter to larger diameter on the discharge line is better than small to large on the suction side.
Before going to the expense and work of adding an electric pump, increase the size of the manual pump intake line to the designed size from the pump manufacturer, probably much larger than ¾".