So the `warbling' is definitely due to an interrupt latency problem.
While looking for this, I noticed that the multicast filter handling
in the CS8900 driver was broken, causing the machine to receive most
or all of the multicast packets being flooded onto the network it's
plugged into.  `Oops!'

After fixing the CS driver, the output is much nicer at 44KHz.  Of
course that doesn't really fix the latency issue.