I was hoping someone would provide a better answer than I can. And you may want to try posting over in the Mechanical forum for more opinions.
It sounds like you want to do these depths as static structurals with different load steps as opposed to a true transient simulation. Based on that, I thought about using the External Data component to do this, but it only allows you to apply this to Imported Load in Mechanical. Another thought was using a code snippet that uses *TREAD command. Search this forum or the help for examples. That may be able to do it.
An alternative, and this is likely a terrible hack, would be to parameterize the value. In the Paremeter Set component, you could then copy and paste the values into this parameter. The downside is each one would be its own analysis and they would not be accessed using the simple changing the load steps. You would have to return to the project page to change the value.
But my biggest recommendation is post this over in Mechanical. There are a lot of eyes over there and someone might have a better idea.