Yes, there are two things that probably contribute here.
One is (as you guessed initially) "storing only a small percentage of the total energy output and giving a diluted price with the partial storage cost spread over the total output." The majority of the solar generation can be consumed immediately without taking a trip through the battery. The battery capacity is needed to serve peak demand periods in the late afternoon/early evening, which last just a few hours.
The other is that you are probably lowballing the number of charge/discharge cycles at 2190. Unlike EV batteries, stationary batteries for grid demand don't ever need to "supercharge" at high rates or rapidly discharge for high acceleration. Careful moderation of charge/discharge rates can give double or more lifetime compared to identical batteries that undergo fast charging and discharging.
Utility installations have much cheaper solutions for cooling, the balancing is much easier with lots of parallel cells, and even the chemistry benefits from smaller charge/discharge currents.
We're not down to $30/kWh yet, but we're not that far off. Certainly well below $300.