Question: Our power meter has two "branches" - one for ground floor and one for upper floor, and on the bill we've got 2 readings, again one for each floor. Also from the street we've got 2 mains cables coming to the meter box. They may or may not be the same phase - how can I tell? This is in New Zealand, typically single-phase 240V power.

The reason is that we are considering solar panels and the single-phase inverters are much cheaper than the 3-phase ones. In fact I don't know if we can actually have a 3-phase inverter with an unbalanced power draw, and with the 3rd phase unused altogether.

The solar people looked at our meter box and they didn't know what to make of it. They suggested to only attach the PV to one of the branches but that kinda makes the investment less efficient as the other floor would get no benefit from the solar panels.

So my idea was to ask an electrician to change our setup to only use 1 mains cable for the whole house, disconnect the other one and then have a clean-cut single phase system where we can use the solar with a single-phase inverter. Does that make sense?

Answer: 
Just put a AC volt meter between the two phases. If it reads zero its the same phase, if it reads 480 Volt they are two opposites of a two phase system with a 180 degrees phase angle.

If you get something in the middle, then the voltage you get should be 240\*(1-cos(a) ). Where a is the phase angle. You can then calculate the phase angle with a=acos(1-Vm/Vb), Where Vm is the measured voltage and Vb is the voltage on a socket, so 240 volt theoretically.
Get a multimeter set to AC voltage. Carefully measure the voltage between the two supply lives, trying not to electrocute yourself in the process.

On a 230V supply, two lives on the same phase will show no more than a few volts. Two lives on different phases will have around 400V between them. It's a bit less than twice the supply voltage.