Is there a battery management strategy that would reflect that the storage of excess electricity should not impact the cost/kW of battery energy?

The system configuration whose operation you describe, where the diesel charges the battery in the first few hours of the year, uses the cycle charging strategy.  Under the cycle charging strategy, the diesels charge the battery whenever they run.  If you do not want the diesels to charge the battery, then you should not model the cycle charging strategy.  You can do that by unselecting the cycle charging checkbox that appears in the System Control window.

If you go to the Optimization Results tab and click Overall, the system configuration that uses load following will appear in the list.  Under the load following strategy, the diesels do not charge the battery except when they are producing excess power due to the minimum power output setting.  In that system configuration, the cost of battery energy is zero and the battery charges and discharges frequently.

Please note that you have specified a very high annual O&M cost for the battery cell stack -- half the capital cost.  You have also specified rather low values for the replacement and O&M cost of the diesels -- $3/hr for O&M on a 1.5 MW generator.  That tilts the economics in favour of the diesels, which will lead HOMER to favour the diesels.  This is partly offset by the fact that you have specified a shorter lifetime (20,000 hrs) than I would assume for a generator of that size.