What you're saying is that you refuse to purchase nail proof tires or drive around the nails in the driveway.
If you're pushing your equipment beyond it's limits then the only solution is to purchase equipment that'll do what you want. If you don't, you can expect problems and eventually it'll shorten the life of the AVR and will turn into a self solving problem unless you replace it with another unit that's not up to the task.
Try running the setup without the rear channels and see if it still trips off. This would help isolate the problem. If your center is also 4 ohms then bypass that one as well.
If you're pushing your equipment beyond it's limits then the only solution is to purchase equipment that'll do what you want. If you don't, you can expect problems and eventually it'll shorten the life of the AVR and will turn into a self solving problem unless you replace it with another unit that's not up to the task.
Try running the setup without the rear channels and see if it still trips off. This would help isolate the problem. If your center is also 4 ohms then bypass that one as well.