Well, here is how I always do these sorts of things...
I drain the coolant from the radiator at the drain plug.
I then service the engine however it is needed (thermostat, lower intake manifold, heater core, radiator, hoses, etc), and then button it all back up.
I then install a flushing tee.
I install it in the hose going to the heater core. I generally install it into the driver's side hose on the Intrepid, because you can get to it to install the hose or install the cap.
I leave the fill cap off the pressure tank, and leave the drain plug open too. I then turn on the water for the hose and then start the car. I let it run till the engine is fully warmed up and the thermostat opens, then run it a bit longer. When the water runs clear out the openings, I shut the engine off and then quickly turn the water off too.
Let the system drain as much as possible, and then install the radiator drain plug.
THEN you fill the engine with 1/2 of the total capacity of the cooling system with 100% full strength antifreeze. So, if the system is a total of 1.5 gallons, I pour in .75 gallons of antifreeze. If the system is 3 gallons, I pour in 1.5 gallons of antifreeze.
In the LH cars, I pour in 1 gallon of antifreeze. I ONLY run Zerex G-05 coolant - but any antifreeze that fits the G-05 standard is acceptable. I do not run universal fluids, I do NOT run DexCool.
You should be able to pour in just about all of the coolant, if not all of it. If you can't get at least 75% of the gallon of coolant into the car, I'm guessing you have a blockage.
After adding this much full strength antifreeze, I then attach a small clear vinyl hose to the bleeder valve, and run the other end of the hose down into the now hopefully empty antifreeze jug. I then add plain water to the overflow tank and watch the fluid flowing through the vinyl hose. I pour water into the coolant tank a little at a time, till I have a reasonable amount of liquid in the jug with the hose in it, then swap jugs and pour the recovered fluid into the coolant tank. I continue to alternate jugs till the fluid coming out of the hose has no bubbles in it. Generally, this doesn't take very long at all.
Every so often I have had to coax the bleed to start, and I've done that by opening the valve, squeezing the upper radiator hose, then closing (or blocking with my finger) the bleed valve and letting go of the hose - then do that again a few times till you end up pumping coolant out of the valve. But it should flow fine after that.