IMO, you could flush your rears first.
Then replace your passenger side front brake line and flush the right front line until clean, attach caliper.
Move to left front, replace line, flush line until clean, attach caliper.
Bleed right front caliper until no air.
Bled left front caliper until no air
Center proportioning valve.
Motor on.
This is all made simple(r) by using a force thru brake bleeder pump. You could use a vacuum bleeder if you can find a way to attach vacuum bleeder to open end of new brake line air tight.
Are you going to upgrade your front calipers and rotors to the gmt900 set up? ( 2007-2014 or 2006 police package brakes)? I hear it is a worthy upgrade. I have all the parts but have not installed them yet. The price difference between 2003 calipers rotors and pads vs 2010 same parts was like 4$.