I was able to replicate the behavior, and my GL wizard office-mate figured out the problem.
Basically, one of the EGL contexts isn't noticing that the texture contents have changed, so it keeps rendering older data. We think it's getting occasional updates because it has a set of buffers that it cycles through, so eventually it re-uses the buffer you're looking at.
I was able to fix the problem in my code by updating the texture renderer class, changing this:
GLES20.glBindTexture(GLES11Ext.GL_TEXTURE_EXTERNAL_OES, mTextureID);
to this:
GLES20.glBindTexture(GLES11Ext.GL_TEXTURE_EXTERNAL_OES, 0);
GLES20.glBindTexture(GLES11Ext.GL_TEXTURE_EXTERNAL_OES, mTextureID);
The un-bind and re-bind causes the driver to pick up the right buffer.