The issue here is not that it is not possible but that the products don't yet really exists for what you want. And may in the end cost more than you would think.
The AC charger on-board the Tesla is rated to 11KW on three phase 3 * 16 amps and 7KW on single phase 32amps(it actually re-configures two of the 16 amp AC charges into a series configuration to get you the 32 amps, but I digress). But here is the trick, the AC charger you are going to install(or the mobile charger that comes with the car) is not a charger at all, it is an Electric vehicle supply equipment (
EVSE) but everyone calls them chargers and it doesn't normally hurt to think of them like that. You already own the 'expensive' bit the 11kw on-board charger. The EVSE is just a smart/fancy power point/cable with a different connector on the other end.
I too am looking at upgrading my solar installation. You are closer than you might think in having a DC to DC system. Take for example the Sungrow 10KW hybrid inverter,
Three phase, 10,000W hybrid inverter with integrated energy management system (EMS).Connect up to 15kW of solar panels to the grid while charging a high voltage (150-600V) Lithium-ion battery bank. The hybrid inverter is rated IP65, meaning it can be installed outside.This intelligent hybrid...
www.rpc.com.au
hybrid being that it can take both the DC solar and convert it to AC for your home, or take the DC solar and charge a DC battery. Co-incidentally this would also give you around 11KW of DC battery charging as it is rated to charge the DC battery at 30Amps and the tesla battery is around 360-370Volts. So Power = Voltage * Current so 30*370 gives you 11.1KW.
Now the issue here is that this hybrid inverter doesn't know how to talk to the CCS port on you car to access the DC battery. With the right smart adapter between the hybrid inverter and the CCS port it is theoretically possible to then charge the car off this hybrid inverter coming directly from the DC solar. As far as I know, no such smart adapter exists.
The way things are going at the moment, with home solar systems often having a separate solar inverter, and then separate AC coupled battery containing its own inverter and what looks like to be the next separate inverter, is another for Vehicle to Grid, V2G, with what is being termed a bi-directional charger. A few of these exist but are expensive, around 10K I believe, and tesla likely, at least for now, prevents current flowing out of the CCS port and allowing its battery to be used in the configuration. Though this should be able to be updated with a software change in theory.
Maybe in the future we will in fact end up with tribrid solar inverters/battery charger/discharger that talk to vehicles and/or home batteries. But I think we are a little way off that. And I could forsee that type of inverter being in the same sort of price range as the sungrow linked above as there is only really one piece missing from that inverter which would be the ability to talk to the CCS connected battery on wheels and maybe an additional contactor.