High Switching - Slow Fall Times

If you want a good looking scope picture, add a 1k resistor from p-channel drain to ground.
Won't make any difference for the LEDs though.

Why aren't you switching the LED strips low-side, with a single logic level n-channel mosfet.

Another option is a PCA9685 breakout board (Adafruit, ebay).
16 channels of 12-bit hardware PWM.
Several boards can be daisy-chained.
Uses two Arduino pins (I2C).
Leo..