Hi Sec,
I'm using the DSP56721 (not the 25), but I also had problems with the clocks on the ESAI, but on core-0. I was running ESAI-0's clock from EXTAL through the internal routing, and the ESAI was simply not behaving correctly (it would run, but would interrupt constantly, instead of after each word, when it should). At the time, I had no idea the problem might be related to the clocking.
I filed a service request, and tech-support could not reproduce the problem, even running my code. I later found out that they were running my code on a non-dual core DSP (a DSP563xx) as they didn't even have a DSP56721 available. They said that the ESAI was identical in the two chips, but obviously they are not. After a few months, the service request was closed, unresolved.
I then found in the data book a mention that certain internal clocking arrangements could be "unstable". I added wires to my board to route the clocks externally, and all of my problems went away. Who would have thought that clocking would cause an interrupt problem. I am currently running ESAI-0 on core-0 and ESAI-3 on core-1 synchronously from the same external clock that drives EXTAL.
The two things I learned:
Don't trust the internal clock-routing for the ESAI, and
Don't depend on tech-support for a solution.
Sorry if that doesn't help you much. It's is simply what I needed to go through to get my ESAI to work.