I have an almost realtime p1 meter connected which shows imoert and export of each phase. I am looking at officially grid connected system only.

We can export up to 5 kW, but you are right, this may not be everywhere and without explicit permission only 500-800 W (EU is going to standardize on 800 W).

I think to use some solid state relais to switch at the zero-crossing.

My main concern is switching several times a day, probably 5-10 times, the panels off and on while they provide >1kW. None of the suppliers can/wants to provide information for this.

I would suggest to install a 3-phase smart meter (like shelly 3em) in your main fuse box, so you could monitor you total consumption in detail. Depending on the local law/regulations of the electrical company you might not but generated energy back into the power grid and if you are allowed it might be limited (like 600/800 Watt max.). There exist electricity meter that only count up - Independent if you give or take energy - be aware!
So if you would see a lager generation of power, than consumption you could - depending on your inverter - can throttle the generation. A smart inverters 'generated max Watts' could be set via RS485 or in the menu. A micro inverter could be regulated via a proper MOSFET on the negative side of the PV-Panel.