Putting it on the output allows the grid tie to work correctly whether there's utility power or not. The growatt doesn't care if power is going from the outpute to the input in bypass mode, and in inverter mode it charges its own batteries from the output to keep the micro-grid stable.
In other words, the growatt acts as a full-service power grid, both giving energy as needed, and absorbing energy as required.
The one downside is that while it does perform this way, it's not rated nor advertised as such - and so far I haven't seen anyone do a deep analysis of it to determine efficiency, or if there are long term negative effects. I do know that the manufacturer and suppliers I've talked to about this will consider the warranty void if a grid tie inverter is connected to the output, they consider it an invalid installation.
As pointed out, though, it does NOT use the charge settings when it's charging the batteries from the output. It will overcharge the batteries if an external system doesn't kick in and reduce the power going into the growatt - either by consuming more of the energy, modulating the grid-tie output, or disabling the grid tie altogether.
If your BMS has configurable outputs, I'd suggest setting one up that indicates when the batteries are getting close to the point where they will shut off to protect themselves. Have that disconnect the grid-tie from the micro-grid using a latching relay or time delay relay so it has to be either manually reset, or it has to wait an hour or two after the batteries stop complaining to turn back on, and if the batteries do shut down at least the growatt only has to deal with shutdown under load, and not under backfeed - and that should be a relatively safe situation.
If your BMS isn't configurable, you can probably just monitor the battery voltage - anything higher than 54v (a bit less than 3.4v/cell) and you shut off the grid tie, and run off battery for awhile. Make sure you have a time delay or hysteresis so it doesn't switch on and off rapidly under sunny conditions - given your loads and power consumption I expect you'd find an hour or two cycling to be safe. These devices are cheap and readily available:
Set the voltage range, then set the startup time delay to maximum (16 minutes for this one) or use a time delay relay to extend that.