There are not many battery based inverters that are actually meant to feed back into the grid. While some people have had reasonably good results using an MPPT solar inverter fed from a battery, I don't think it is a good idea. You really don't have any control over the power it will try to export. Their whole design is built around trying to get the max from a solar panel. Some will max out their rating when power from a battery, some might actually burn up from it.
I did a lot of searching and I just kept coming back to the Schneider XW-Pro. Yeah, it is a bit more expensive, but it is a beast. It can run up to 6,800 watts all day long. It can back feed the grid while being fully grid code and UL compliant. It meets every safety spec, and it is quite efficient for a unit rated for that much power.
When I first got mine, I just installed it on it's own breaker in my main panel. I would tell it to charge, and then at 4 pm, it would switch to export and push a constant current into my main panel. Either until the battery ran below the set limit, or the time hit where I block export. But the one problem is it won't start a charge cycle by itself. You need to have some other device or a human tell it to charge. It is a dumb software choice by Schneider. I programmed a small PLC controller to manage the charging. I went a big step further. It monitors the energy in my home and commands charging when my solar panels are making more power than my house is using, and adjusts the charge current to keep my grid export to under 100 watts. After 4 pm it switches it to export mode and the PLC constantly adjusts the export current to keep my grid export right at zero.
There are a few other inverters that can do things like this, but they are not any cheaper. Many of the lower cost units can only output power to loads on their output side, not pushing current back to the grid input side. If you can move most of your loads into the sub panel on the inverter output, then this could work for you to nearly zero your grid power. But I have a few large loads back in my main panel, and it really is nice to just have the inverter push the power back to run those loads.