For anyone interested, here is how to do the same with the built-in audio card in Pi 3 (less the mono downmix, look above if you want to add it).

As of today, and quite unfortunately you have to comment out "audio_pwm_mode=2" in config.txt. PCP has a tendency to reinstate that setting when you select "analog audio" output for Squeezelite. Check the setting is still disabled if suddenly mixing doesn't work anymore.
Since AQ is rather poor without "audio_pwm_mode=2", I'd recommend enabling "disable_audio_dither=1".
Here's hoping audio_pwm_mode will come out of beta one day; it looks like the goals for general release are to slash GPU usage and offer concurrent access.

With that done, the following gives concurrent access to the audio card (I tested with 2 streams) and separate volume controls:
Code:
# default - Generated by piCorePlayer
pcm.!default {
	type plug
	slave.pcm "hw:0,0"
}

# PCP3.2: squeezelite gets set to use this device ("-o equal")
# when equalizer is activated. Same name, new type of device.
# This softvol allows to ramp down-up music when an application
# plays another sound.
pcm.equal {
	type softvol
	slave.pcm equal_real
	control.name musicvol
	control.card 0
}

# Same story here: ramp up-down the sounds sent by applications
pcm.gong {
	type softvol
	slave.pcm equal_real 
	control.name gongvol
	control.card 0
}

pcm.equal_real {
        type plug;
        slave.pcm plugequal
}

pcm.plugequal {
        type equal;
        slave.pcm "plughw:0,0"
        controls "/home/tc/.alsaequal.bin"
        library "/usr/local/lib/ladspa/caps.so"
}

ctl.equal {
        type equal;
        controls "/home/tc/.alsaequal.bin"
        library "/usr/local/lib/ladspa/caps.so"
}
(and the same weird but harmless double-free error as reported above.)

HTH