Ok, I may have found a lead. The datasheet for the RTL8211F references a “WOL Application Note”. I couldn’t find that for the RTL8211F, but I did find it for the related RTL8201F. It looks like these might have the same configuration interface.
From the application note, I think I just have to change the number written here to 0x0400 to get unicast mode. Possibly I may also need to write the MAC to some other registers.
I’ll have to play around with recompiling the kernel to try this out.
Ideally ethtool would be able to set the different modes.