but it seems like big overkill for me to have Apache running CGI script which "embeds" www client which requests data from other apache instance.
You say overkill, I say classic application stack. For the past quarter century or so we've been working to a greater or lesser extent with this setup where the user/client/browser interacts with the web server(s), behind which is the application server(s), behind which is the data source(s). There are other ways for sure but this is by far the most common basic setup I have seen across many installations. You already have the backend sorted by the sound of it so adding the lightweight front end should not be "overkill".