I'm building an RGBW LED floodlight.. which in function is really the same thing as your design.
What we need to know is the type of LED strip and it's wiring. What you want is is each color to be an isolated circuit, with the LED's strung together in series and both the positive and negative connections available. Your current supply circuit feeds the LED's positive and your PWM transistor acts as a switch between ground and the LED strip. Given that number of LED's and the currents/voltages, you'll probably break it down across several supply/sink setups to keep it reasonable.