We understood what you want.
What you are asking for is not different at all. It is a standard system.
The stored power is not going to the grid. Only the "extra power" goes to the grid.
Otherwise the inverter would run the batteries flat, which a decent GT inverter will NOT do, because that is not what anybody wants to do.
Two general choices.
First is a battery charging RE system that sends the extra power to the grid.
Second, pretty much sends all the power to the grid, only keeping enough to keep the batteries full.
Either way, the RE keeps the battery full, and anything beyond that, the excess, goes into the grid. The steps may be in a little different order, but the end result is about the same (full batteries with the excess going to the grid).
You seem dead set against #2, but I figure it is probably more efficient for anything large enough to bother with grid tie.
That type of inverter tends to have a higher voltage input, so less conversion and line losses.
I have a feeling by "affordable", you mean those non-UL listed things, and you read they took the 24V bank flat. That is because the dudes selling those things seem to have no idea how they were intended to actually work in a real system.
Unless there is a real good reason to have 2 battery banks (like one bank is a 19.2V nicd or something), then it is more efficient to combine both banks into a single bank.
If there is a good reason to have 2 battery banks, the second bank still needs it's own dump load controller.