I knew that you could retrieve the parameters passed into Test Execute, but I guess I was operating under the assumption that only valid parameters would be passed along. Perhaps I'm wrong, which would be a good thing.
You can do this. Just pass a zero-based index of the needed parameter to the ParamStr method to obtain the parameter as a string. In your example, you can get the '/somecustomparam' parameter in the following way:
<font class="small">Code:</font><hr /><pre>...
var myParam = BuiltIn.ParamStr(2);