Ethercat drives not responding, mesa error finishing read

I can try it, but since ethercat at the command line (linuxcnc isn't even running) shows ~50% lost uploads, what's the point?

I don't think this is a linuxcnc problem, but rather some networking or drive problem.

So you built ethercat master from source? Rebuild with the option --disable-eoe or something that makes it exclude eoe.
The three lines you showed from the syslog says it want to establish eoe network interfaces. Disable that.

Since you have problems with the Realtek adapters, here is a tip.
Add an Intel PCIe network adapter. Of course you need a free PCIe slot. With an X4 slot you can use a board with multiple interfaces.
And if you only have an M.2 slot you can use that forum.linuxcnc.org/18-computer/55782-adding-a-m-2-ethernet-port
 

You mentioned you should have an Intel driver. In which case the R8168-dkms won't be installed or do anything. Start at the beginning

what doeslspci | grep -i ethernet

report?