Im not sure the flow of coolant is in the direction you noted. I think it might be the opposite. But that is really not the point. I would verify that the coolant gauge is working properly especially when the vale is closed. If gauge is operating correctly and the motor has NO other coolant issues, I would use a shut off vale that moves the flow of coolant to the other hose instead of just shutting it off completely. You could probly find one that does exactly that or design it yourself by T-ing both hoses together b4 the shutoff itself. Im not familiar with the pressure type valve u listed but I think the 1st valve would do exactly as I stated.