Chagrin:
That particular chip (PT4115) doesn't do well on the low side when fading it. Tends to shut off at about 20%. I was kinda impressed that OP got his to 2% but then I suppose that was due to burning all that power in the FET.
I don't remeber details as I just used that driver to prove a concept, however the reduction in dimming range for most LED driver chips comes from using a higher PWM frequency. The PT4115 has a dimming range of 5000:1 but only at 100Hz PWM frequency. I drove the PT4115 ( well, actually three of them) from a PCA9685 I2C LED driver that has 16 12-bit PWM outputs where I could change the PWM frequency from 40Hz to 1KHz from my library.
IIRC the normal Arduino PWM frequency is 500Hz so some reduction in dimming range can be expected.
I may have said this before but when trying to control things directly with PWM the standard Arduino boards are not the best boards. The Teensy 3.0 and 3.1 have 10/12 PWM pins with PWM resolution up to 16bit and configurable PWM frequency. The Teensy LC that will be released in March will offer a few less PWM pins but also likely at up to 16bit for about $12.
The Teensy 3.1 uses a ARM cortex M4 32bit MCU and the Teensy LC will use an M0. These boards offer many more things at full Arduino compatibility that you'll be pressed hard to find on any other Arduino board and definitely not at such low cost or size.