This is interesting — you’ve basically described one of the reasons I started developing AION EMS Zeus for Home Assistant. 
Your approach of combining historical household demand, solar forecast uncertainty and current battery SOC to project a range of possible future SOC trajectories makes a lot of sense to me.
One thing I’ve found while developing Zeus is that the difficult part isn’t producing a battery forecast — it’s knowing whether that forecast was actually any good.
Zeus now works around a similar loop:
Observe → Learn → Predict → Recommend → Verify → Improve
It learns household demand from Recorder history, uses solar/weather forecast evidence, knows usable battery capacity, SOC and real charge/discharge limits, accounts for learned battery round-trip efficiency and tariffs, and produces an advisory future battery plan.
We recently added a Forecast Explorer specifically to compare the forecast with what actually happened afterward, including forecast error/uncertainty. Zeus deliberately keeps the original prediction so it can be evaluated later rather than quietly replacing yesterday’s forecast with today’s knowledge.
Your 10th/50th/90th percentile idea is particularly interesting. I’ve been moving Zeus in the same direction of showing an expected result together with an uncertainty range rather than pretending a single SOC prediction is certain.
At the moment Zeus keeps battery planning recommendation-only — it doesn’t automatically force-charge/discharge the inverter — because I want the prediction/verification evidence to mature before allowing that intelligence to control hardware.
If you feel like experimenting, have a look at AION EMS Zeus. Your Sungrow SH10RT + 25.6 kWh battery + Solcast setup would actually be a very interesting system to test it against, especially because a battery that size makes multi-day SOC forecasting genuinely useful.
And I’d be interested to compare Zeus’s learned demand/forecast behaviour against the Monte Carlo approach you’ve already built. That’s exactly the kind of real-world comparison that can improve the project.