Using BC327 instead of BC337 but not working as expected?

The datasheet for the MT7201 says of the ADJ pin:

Multi-function On/Off and brightness control pin:
? Leave floating for normal operation.(VADJ=VREF=1.2V giving nominal average output current IOUTnom=0.1/RS)
? Drive to voltage below 0.2V to turn off output current
? Drive with DC voltage (0.3V<VADJ<2.5V) to adjust output current from 25% to 200% of IOUTnom
? Drive with PWM signal from open-collector or open-drain transistor, to adjust output current. Adjustment range 25% to 100% of IOUTnom for f>10kHz and 1% to 100% of IOUTnom for f<500Hz
? Connect a capacitor from this pin to ground to increase soft-start time. (Default soft-start time=0.8ms. Additional soft-start time is approx. 0.8ms/nF)

So you should be able to get 1% to 100% of Iout using the Arduino default PWM frequency of 490Hz. Note that the PWM will work in reverse, i.e. analogWrite(pin, 255) should turn the LED off, while analogWrite(pin, 0) should turn the LED fully on. I'm assuming that you haven't bypassed the bridge rectifier in the current regulator, that's why I included the diode in the circuit (to prevent Vadj going more than 0.3V below the ground connection of the MT7201).

To drive it from a TLC5940 I suggest this circuit. I've moved the diode to the emitter so that you can share 1 diode between all the channels.

To avoid breaking off the ADJ pin, I suggest you use a fine enamelled copper wire to make the connection to it.