Is there any way to set a minimum battery depth of discharge from the simulation?
Yes, you can set that parameter when you create a battery.
In the Battery Inputs window, you can select the battery type from the drop-down box. When you do so, some of the important properties of that battery appear in the area below the drop-down box. But those are not all the properties of that battery. Click the Details button to see all its properties. The minimum state of charge is one of those properties. You cannot change any of the properties of an existing battery, but when you create a new battery you specify all of them.
Click the New button to create a new battery. (It will create a copy of whatever battery was selected when you hit New. You can change only a few parameters or change everything.) In the Create New Battery window you define the properties of a battery, and from that point on that battery will appear in the drop-down box of battery types on the Battery Inputs window.
If the battery you want to model is already in the list of batteries but it has a different minimum state of charge, then select that battery, click New, and set the minimum state of charge to whatever you want.