I have been using a hand-pump but I want a more effective way to swap out the ACE fluid.

Should I just take off the reservoir hose, point it down and shake the car side to side until it doesn't pump anymore fluid out of the hose? Sounds like a pretty ghetto way of doing it but I'm up at college and don't exactly have a ton of tools to work with.

 

I wouldn't drain the system. You risk damaging the pump and how do you plan on bleeding the system when you refill it?

I would drain and fill the reservoir, drive it and repeal. eventually you will flush most of the fluid in the system.

 

I've went through around two full bottles of fluid and it still comes up dirty after 5 minutes of driving.

 

Not necessary to drive between fluid exchange in res( though it works fine)
You can manually rock the brick, side to side, while truck is running

 

and if you want to flush your system too bright pink it is going to take you a lot more than two quarts. treat it as you would a transmission, plan on changing it all out over a period of time.
get a turkey baster pull out a quart from the pump and replace it every couple weeks, until its clean enough.
or your going to need something like a hawkeye that will do an ACE bleed