Solution - back off the channel gains, and increase the master output.
I've found that if I set the channel gains to read 0dB with EQs flat, then master out also to 0dB, increasing the EQs causes compression and distortion.
BUT - if I set the channel gains lower than 0dB, and increase the master volume, then I can happily use lots of EQ without the master overloading.
It's odd, but it's true.
I have now demonstrated this live to Simon from AA (UK) and he agrees. He will be reporting it back to AA to see if it can be fixed.