A small heatsink in combination with a case probably doesn't result in enough cooling as cases usually block airflow. You could try without the case, turning the RPi by 90° so that the GPIO connector is on the bottom can also help improving airflow (some time ago I did some tests and got 1-2°C lower temps with this setup).
I don't think the RPi audio cards will work on the tinkerboard as it's missing the drivers for it.
I'm using plain Kodi to play audio, in combination with Yatse on an android phone or tablet - this allows for easy remote control without having to turn on the TV.
I can't complain with audio quality when using Kodi, I'm mainly using FLACs and audio output from Kodi is bit-perfect. IIRC most reports of Volumio or other audio distros sounding "better" boiled down to them having configured a higher output volume - compare the with amixer values, this should give you a hint if that's the case.
AFAIK there are not "equalizer" addons for kodi, some time ago Kodi supported DSP addons but that was dropped as it wasn't working properly IIRC.
so long,
Hias