I would first try what @DaneLLL suggests. It is possible that the other driver is optimized differently, or just changes timing such that it is more efficient under load.
In terms of changing which core the ethernet runs on, I don’t think it can be done (I believe that if the commands to force to another core succeeds, then the scheduler will just move it back to the original core after checking the desired core and finding it cannot go there; it wouldn’t hurt to try though).
For other software which is not dependent on CPU0, if you find something with significant CPU load, then you can look up the topics of “taskset” and “CPU affinity”. See: