You should connect in series with power line special thermistor, as in tube monitor PS.
http://www.littelfuse.com/products/temperature-sensors/power-thermistors.aspx

Thanks! ... I had a very vague recollection that such devices needed to be used in cases such as this. According to the sim, inrush current peaks at 35 amps 1ms after startup.

 

Thanks! ... I had a very vague recollection that such devices needed to be used in cases such as this. According to the sim, inrush current peaks at 35 amps 1ms after startup.

It is routine work of electronic circuits designer .
Thermistor will help to decrease inrush current.

 

It is routine work of electronic circuits designer .
Thermistor will help to decrease inrush current.

It might be routine to you ...

Anyway, I picked this model for this application. It's rated for a steady-state current of 3A, which is more than enough.

 

Anyway, I picked this model for this application. It's rated for a steady-state current of 3A, which is more than enough.

Good choice. They are very hot in working state. Sometimes I placed them in box from power adapter and used this box as power cable connector. It decreases temperature inside of device.

 

Good choice. They are very hot in working state. Sometimes I placed them in box from power adapter and used this box as power cable connector. It decreases temperature inside of device.

I've just noticed that, according to the sim, a peak 4A flows from the supply when the device is working at 50% PWM. So I've decided to also buy a few 7A limiters too, in case the 4A thermistor obstructs normal operation. What do you think?

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Does not matter what is peak current. They have big thermal inertia. You should calculate RMS current.
3A RMS or lower is good.
Best current for them is nominal (3A RMS in your case). At this current they have minimal working resistance.