Hi
The hose in your picture is a make up hose.When the cooling system cools off the coolant shrinks and pulls coolant from the tank.When the coolant gets hot it expands and fills the tank.
Just for experimentation use the lines for your heater to try your theory.
When it doesn't work like you want you can return it back to stock and try an external water source and pump to get the results you want.
As mentioned before the cooling system in your truck is marginal at best when these trucks were new.Messing with the flow or changing the flow will not help your engine when you add more fuel and air to it,resulting in more heat for the cooling system to deal with.
90 Chev 3500 c/c 4x4,6.2na,400 auto,4:10 gears.DSG Timing gears,main girdle, isspro tach, pyro,boost,oil and trany temp.Dual Tstats, High volume peninsular pump,on shelf, Custom turbo and intercooler 85%complete. Change of plans for the dually, it's going to get a Cummins. Both trucks are Blue 90 4x4 crews