>one thing that pops to mind is that somehow the ethernet connection to the modem negotiated in half-duplex.
The data rate is 1Gbps (or 100Mbps for older routers). Transferring 10KBytes/sec would be on the order of 100kbps of data which would only take up a tiny fraction of the time slots. That's 0.1/100 or 0.1/1000 of the time slots.
Same type of linear thinking reasoning that tell people to check Ethernet cables or the power supply when the person can see the modem webpage. A big waste of time that shows that you can't debug systematically.