I have seen this a couple times and there are one or two things to keep in mind.
The UP5000 battery is designed to output around 2.5KW (50A discharge as indicated in manual). This can cause some confusion because a user will read 5KWh and assume that the battery can output 5000W. Once the load exceeds this value, it will cause a sharp voltage drop (even when it is only a momentary "spike").
So what tends to happen is that the inverter picks up this "voltage drop" and assumes that the battery has reached its "point back to grid" and then gets stuck waiting for the "point back to Battery" set point. Also note that when this happens, the battery voltage will pop back up as soon as the inverter transfers to grid (removes the load from the battery).
I understand that you mention that the load is linear so this should not be a problem but I figured it best to have this presented for clarity.
Having the back to grid voltage at 48V will leave your Lithium battery SOC rather high (probably around 75%). I have changed mine to a lower value to allow the inverter to make use of more of the stored power. See the image attached, it indicates that the battery can operate between voltages of 44.5V to 53.5V so allowing your inverter to draw from the battery to a voltage of 46.5V should not cause any issues. This does change the depth of discharge that your battery is operating under and would give you more usable wattage while the grid is available.
Should this be the preferred solution, then it is important to note that you will also then have less reserved energy available should you experience a power outage at night time.
You are welcome to contact me directly for a more detailed look at you situation. https://mecadon.co.za/wp/