Hi, Matt here and can help you (software developer for 21 years).
What you need is a simple PHP script on your web server that will act as a web service - your desired automation can not be done within Excel or Windows itself.
So you need to provide working PHP interpreter with CURL library so that:
1. VBA macro calls your custom PHP script that will visit your web page, log in, open a table, post a value and retrieve resulted table.
2. Resulted table is returned to Excel (VBA) as a formatted string.
3. VBA function parses the returned string, counts the number of elements (to get a cell range) and fills values into a range of cells with a defined first cell.
That's what I can do (haven't for some time).
Is this solution workable for you? Or you would rather have pure client e.g. desktop solution without requiring a web server script? Then it would be possible to automate your process with automation software (proposing Sikuli or AutoIT). The issue here is how to integrate this into Excel e.g. it would be the other way around - calling the automation script via at (scheduler in Windows) that visits the web page, retrieves the data, opens an Excel file and fills it with returned data.
No costly security options are needed - PHP script is protected (source) by default while you can easily restrict access to your website script if you are using fixed IP address in your company. That might limit access from anywhere though.
Looking forward to hear your opinion,
Matt