Each level of battery min SOC requires a new battery model.  Is there a way to find the best min SOC in a single run?

Because the battery mfgs cannot give us really complete data on how low SOCs kill their battery we treat it just as a constraint.  If you relax that constraint HOMER thinks that is great, so it will almost always prefer that.  We don't really have any way of trading off the benefit of low SOCs (more energy throughput per $ invested in batteries) against the cost in lifetime.