Well, I thought this one would be easy. But it isn't.
One thing I think you have misunderstood is that linked Zones don't play through each other. All linked Zones are played to at the same time.
So your Headphones Zone with its DSP can be played to.
Your AVR Zone with different or no DSP can be played to.
When you Link those two Zones, both are played to, at the same time. One with DSP and one without. You aren't sending the output of MC to the Headphones Zone, and sending the output of that Zone to the AVR Zones. Think about it; where did you define which Zone comes first? Hence what you hear as output on the AVR, whether via speakers or via the Headphones plugged into the AVR, is the AVR Zone output.
Consider this: You have some stereo outdoor speakers, and you have 5.1 speakers in your loungeroom. Each have there own DSP settings. When you link them, the output of MC goes to the Outdoor Speakers Zone and is downmixed to stereo, at the same time the output of MC goes to the Loungeroom Zone and is played in 5.1 surround sound. At least that is my understanding. I'm not running linked Zones.
Beyond that my head spun.
The only way I could think of doing what you wanted would be to set up two DLNA Servers in MC, one with DSP (Headphones) and one without (Normal Playback), and then switch DLNA Server on the AVR when you need to.
It is quite possible I am wrong in this. Someone else may come along and correct me.