Interesting. Breville has said they will replace it, but unfortunately their techs don't share service info with Customer Service, so I'll be unable to find out what ends up being defective or broken. I may have a day to tinker with it before the new one arrives though.
So whatever the problem is, it can only be between the pressure tap for the gauge, and the group itself. So whatever it is, is confined to a small area that we can't see the inside of, like group complex. Or the puck itself becoming compacted and choking the flow as suggested. Though I've not actually seen that happen myself. Did you say it runs normally holding steady seven bar when you use a pressurized basket? If you happen upon some more coffee, even some cheap Maxwell house or grocery store brand, try pulling a shot without the screen or dispersion disc. If the problem does not exist there, then put back the dispersion disc but not the screen, and pull another. And so on.
Just some general systems knowledge: If the solenoid were to de energize and the pump keeps running (this would be a wiring fault unless you set it up that way on purpose like I did), you would get no flow even though the pump is running, BUT you would also read no pressure. IIRC, you were saying that you were getting climbing
pressure and declining/no flow, correct?