Photoshop :: Batch Overlay Multiple Images

I'm an architect and would like to automate a process we do all the time: shadow studies.

Here's a typical scenario: we render a view of a building, same camera angle, just changing the time of day for each rendering. Then we take those renderings and overlay them in Photoshop setting each layer to "Multiply", add a Brightness/Contast or Levels adjustment layer, and save said image. We do this for three times a year (one equinox and each solstice), often a few views of the building for each.

So a typical shadow study might be 4-5 views, three times a years, so that's 12-15 composite images. This process gets repeated multiple times for each project as we change the design, so there is a lot of repetition.
 
I know how to create simple Actions. I know how to run a batch. What I don't know how to do and would like is a way to run a batch where I select some files and it creates the composite. The hurdle is making the Action and Batch be "generic" so that when I run the batch, I can select the images I want and the place to save it. That's the part I don't know how to do.
 
The Action I created is limited by (a) files open and (b) therefore only applicable to a certain number of open files (if I create the Action with 4 open files, it will only work on 4 files, not 3, not 5).
 
If required, I could probably script something. I know some programming/scripting, but have never done it for Photoshop.