I had some trouble with the accepted answer as I'm not hugely familiar with shell scripting on Android/Unix/Linux so I thought I'd add my experience here for anyone in a similar boat.
To get this working with Tasker or similar the line you need is:
echo 0 > /sys/class/leds/lcd-backlight/brightness
For tasker put this in the 'command' field with 'Use Root' enabled, works like a charm. To disable simply switch the zero out for a 1, ergo:
echo 1 > /sys/class/leds/lcd-backlight/brightness
or lock and unlock the device.
So to answer your question about quickly toggling this behavior. Assign each of the above commands to a tasker task, then you can make use of the new long-press intercept in the latest tasker version to toggle the screen on and off without putting the device to sleep. Alternatively you can assign the command to a profile which triggers when your conditions are met.
/sys/class/leds/lcd-backlight/brightness
to 0 does the job in my device. It doesn't put the device to sleep, but simply turn off the LEDs. Tested on that Calm app. You can hear its music yet not burning up the battery on screen. Requires root access though.