THALL The issue is the total output capacity of the inverter clipping the solar input. It's not unusual to see generation numbers well into 5+ kW from my panels on a good day, and I've seen as high as the low 6s. This is only possible when the AC output of the inverter maxes (about 3.8kW in reported value) AND the battery can take a full load of DC, since the inverter seems happy to shunt DC into the battery before converting to AC.
Once the battery is full, the most the inverter can push out is 3.8kW of AC, regardless of how much the panels are producing.
Thus, on a day like today, if I leave the system in mode 1, the battery is full by 1100 or so at the latest (when the panels start to peak production due to the two-roof layout) and the inverter clips the output to 3.8kW regardless. If, however, I use a timed export in the morning to prevent the battery charging up until the point when the inverter is maxing out, I can effectively harvest over and above the limit of the inverter by giving it the battery as a DC receiver for the excess generation.
You're correct that everything over what I'm using goes into export, but that's still limited to the inverter's maximum AC output.
Taking today as an example, I ensured the battery was empty until about 1100 which allowed me to export in the morning rather than charging the battery. I then switched to mode 1 to allow the battery to charge whilst the panels were exceeding the inverter, and then the system clipped to 3.8kW once the battery was full. Today that meant about 3-4 hours where I know for a fact the PV was producing more than I could actually get through the inverter. It'd probably only have been another 4-5kWh but I'm guessing at this point.
The solutions for me would likely be to either switch to a 5.2 Hybrid inverter, which could AC convert almost everything the panels produce, or add a second battery to give more DC pre-inverter capacity. The extra battery is probably the more useful in both the shorter term and longer term, until I add more generation.