Try building a test kernel with an added SW-quirk for the ASM1062, like described here:
Here's the summary from my chat with Gemini. I don't remember specifics from when I did it, but this summary seems accurate from what I do remember. Obviously proceed at your own risk, but it has been working fine through multiple reboots for almost 2 weeks for me now. Depending how you set up your VMs/LXCs and if they rely on mount points from your NAS VM, you may have to set up a boot delay to give it time to start up.
I am by NO means an expert in any of this! I just asked Gemini a lot of the right questions to get it going the way I wanted to. So as much as I'd like to, I...
Just replace the device ID mentioned in the linked thread (i.e. "0x1164"), with the one of the ASM1062. Then see if it works.
Could be, that this behavior is a ASMEDIA speciality.