Ed,
There are a couple of questions i need to ask, and a couple of suggestions...
When the M4 is being run, has uboot running and has linux booted? uboot will enable and configure one of the enets, because it has the capability for a tftp boot-up. If linux is running, then the linux driver will be working against any efforts made by the M4 on the enet hardware.
I believe uboot uses enet0, so doug's experiments would be better suited for enet1. This way there are less chances of any other code getting in the way.
The original question, there should be nothing stopping the M4 from getting to the enet registers. The RDC, which would prevent access, is not setup for exclusive accesses in uboot, or in the enet drivers.
If linux is needed, then the dts/dtb file needs to be modified to turn off the enet that the M4 would like to use.
Let me known if you have additional questions,
mark