Sort Pivot Table by first and third column only

I have a price list set up on a pivot table. The pivot is grouped by product type (first column) followed by the SKU/ID and then by the product name. The remaining columns are not relevant to this question. Excel automatically sorts the pivot by Column 1 (Category), then by Column 2 (SKU), and then by Column 3 (Product Name). My problem is that I don't want the list sorted by SKU, just by Category and Product Name. Is there a way of doing this without having to create a separate rank column which I then will need to hide? I have tried changing all the other sort options available to no effect and, unfortunately, changing the column order is not an option for me.

Thanks!
Alex

Sorry. Here is a sample file. Like I mentioned originally, is there a way to sort the pivot without having to resort to additional columns which will need to be hidden?

Thank you Andy, I suspected that this was the case but hoped that there was some sort of setting that would allow one to bypass the default sorting order