I remember years ago, my dad had an old chevy celebrity that blew a head gasket or something so a bunch of oil leaked into the coolant. After he got it fixed, he got a Prestone kit that had a T-connector that you cut and install inline on one of the coolant hoses, and a spout thing that replaced the radiator cap. The T-connector was threaded for a garden hose, so he turned on the water, started the car & flushed the whole system til the car was up temp.
Obviously that kit wouldn't work on our trucks, as we no longer have radiator caps, but you could probably do something similar with a hose in the coolant bottle as Bucko suggests. You can run an engine with the drain open, as long as you're filling it at the same time. I would probly use just the radiator drain.