I changed all my own hoses and did the stat, too last Fall. Emptied it all out, took the thermostat out, let the car cool, started it, ran the garden hose through the radiator and through the thermostat housing to flush it all out, emptied all the water, refilled with 50/50 Honda fluid (for an Integra) and was on my way.
Check your Chiltons, Haynes or similar manual, which should have a specific flushing procedure for your car. Its not a bad (or as messy) as it seems. Takes 2-3 hours of time.
And regarding the waste fluid, youre NOT going to have to get rid of 15 gals of fluid. When you pop all the drain plugs and take off the hoses, you should be able to remove (and colelct) at least 80% of the "bad" fluid which your car holds. The water youre flushing with isnt terribly contaminated. Mine ran clear after about five seconds of "flush" time.