I think you need to verify the accuracy of that LCD meter, say against a digital multimeter, preferably a half decent one. You seem to have a large discrepancy between the LCD meter and the inverter.
It sounds like your inverter's battery voltage measurement is way off. I have no experience with the smaller models to know if that's common or not. When charging LFP with their very flat voltage versus SoC charge curve, it's more important to have an accurate battery voltage reading.
After verifying the accuracy of the LCD meter, I would attempt to calibrate the inverter's battery voltage measurement. Details are here. The problem is, I'm not sure that these tiny inverter models have the required command. If you tell me your main (DSP) firmware version (U1 on the front panel), I might be able to tell.
The other thing is that as long as the voltage readings are consistent (and don't vary with time and temperature), then you can just translate the reading and change the settings to whatever it takes to get the required bulk/absorb voltage. The premature float bug should not affect utility charging, and you have not mentioned solar charging at all. Though make sure that maximum charge current (setting 02) is the same or nearly the same as the maximum utility charging current (setting 11). If setting 02 is greater 5 times the setting 11, then the premature float bug WILL manifest with utility charging (that's the way to demonstrate it). But I don't think your model can even go that high.
LFP batteries don't work that way. When they are truly full, then it only takes a tiny current to push them to 3.6 VPC (14.4 V for your 4S battery).
Again, LFP doesn't work that way. The upper voltage plateau is about 3.33 VPC, so that's 13.3 V for your battery. It could have that voltage and only be about 70% charged. You can't use voltage to guess the SoC of an LFP battery, except at very high or very low states of charge. 8 amps is only 0.04C for your 200 Ah battery, so it will take a long time to charge at that low rate. BTW, 20 A seems very low for a maximum charge rate for this battery. Usually LFP can charge at about 0.5C, which would be 100 A. Not that your inverter can probably charge that fast.
That's the other thing about LFP chemistry; the voltage relaxes after charging. If it has Yttrium added, it may relax less, but I don't think that most manufacturers use that additive any more. This does NOT indicate a loss of stored charge.
There is another voltage plateau at about 3.30 VPC (from poor memory), which is about 13.2 V for your 4S battery. My guess is that you're not charging the battery enough.
You might be making the rookie mistake of believing the SoC reported by the inverter. That figure (when you're using an LFP battery) is only for entertainment. It's really rough if you have a lead acid battery; for LFP, it can barely tell you the difference between totally full and dead flat. Higher power models come with a way to talk to the BMS of the battery (if present), and that can give a much better estimate of SoC.
That's about 3.22 VPC, which is just above the nominal voltage of the cell (3.2 V). Personally, I let mine go down to the equivalent of just over 12.8 V, which is about 20% SoC if it's being lightly discharged.
Remember: LFP ain't lead. You can't treat them the same.
I just hope I don't have to resort to changing the float voltage to what I want the charge voltage to be every time load shedding hits, and then back to what I want the float to be after the battery has been charged.
I can say that it carried a 400W (35 Amps/hour) load last night for the 2 hour session and the battery was at 12.9 (+- 20% SOC) before the power came back, this still seems as too much drain for the rated capacity of 200AH, so lets see what the changes bring and then I will report back.
Thanks again.
