It's a bit complicated, but I ended up getting a Goodwe GW5048D-ES single phase hybrid inverter. It has two MPPT PV inputs, takes a 48 V battery, and can push 5 kW AC out continuously.
The problem is about one in three homes in Perth are wired up for three-phase (415 V phase to phase, 240 V phase to neutral). My house is one of these. The supply feed is 6 mm2 cable, so I'm good for about 22 kW in either direction.
However, three-phase hybrid inverters aren't common, and those which run on low voltage battery packs are even less common and are also more failure-prone. Moreover, our network provider (Western Power) has set a limit as to how much power you can push back during the day, and how much phase imbalance you are allowed. In my case, it's a maximum phase imbalance of 2.5 kW meaning a 5 kW inverter on one phase is not on.
However, if you have a battery, they let you increase the amount of PV, increase the size of the inverter, and allow up to 3 kW of export on a single phase. SO yeah, it's messy. But the system is approved for 7.9 kW of solar, a 5 kW hybrid inverter one one of the phases and an allowance of up to 3 kW of export. The export will earn me 7 cents per kWh, or about 60c on a good day. The network connection fee is $1 per day.
My preferred system would be a 25 kW three-phase inverter with low voltage battery storage, but most seem to run 400-600 V DC batteries for this. Makes sense - lower losses in the conversion. But high voltage battery packs are a PITA.
I also have an EV I want to charge, so provided self consumption is optimised I should only be leaning on the grid for 4 months of the year, and coming out in front all other times.