Again, why not simply replace it with another Darlington?
Please post a schematic.
Why replace the Darlington? Why not, who knows I might even learn something.
Because there is no need to. A MOSFET is an inferiour choice in that circuit.
A schematic is hardly worth it. It's like I said, a R/C into a Darlington, now changed to Sziklai driving some LEDs. But ok
The schematic is worth it. No one knew what you were on about before you posted it.
You mentioned using the MOSFET on the low side. This is why it gave a sharp turn on. It had nothing to do with the type of transistor. The difference is in your schematic, you have the transistor configured as a follower, which has a voltage gain of just below 1, which buffers the capacitor voltage to the output, minus the threshold voltage. Moving the transistor to the low side, converts it into a common source/emitter amplifier with a high voltage gain, hence the large suddent change in voltage across the LEDs for a small change in voltage across the capacitor.
You could swap the Sziklai for a low threshold voltage MOSFET and it would give a similar response, but it will still have a greater voltage drop, due to the threshold voltage being slightly higher than the Sziklai pair.
If you really want to learn something, then redesign the whole circuit to use a microcontroller and dim the LEDs with PWM, using a MOSFET.