It seems you're using the wrong parts to control LED strips.
That chip if for direct driving small LEDs (sink only).
And the fet is not a logic level fet, so can't be driven with 5volt logic.
A PCA9685 breakout board (Adafruit or ebay) could do what you want.
16 channels of 12-bit PWM with 2-wire I2C control.
It can directly drive the logic level mosfets for your LED strips.
Leo..