Have you done everything shown on their github site. While you cannot use the provided install and service files, you should do everything they do manually.
https://github.com/waveshare/WM8960-Audio-HAT1) Driver built - This appears to be ok
2) dtbo installed in /mnt/mmcblk0p1/overlays
3) in the boot config.txt did you add dtoverlay=wm8960-soundcard
4) Assume you have also enabled both i2c and i2s interfaces.
5) Add the asound.conf to /etc (Also add etc/asound.conf to /opt/.filetool.lst)
6) Copy the provided asound.state to /var/lib/asla/asound.state (Make sure to add this file to the backup list too)
Then during boot, you will need to wait for the card to be recognized first
Then restore the asound state.
Let me know if you need more direction, but just follow what they do on github. And convert what they to do tinycore methodology.