Actually, I was able to include the Product code in our POs (as we have the product code saved in both the "Item Code" and "Product Name" (or whatever QBO calls it)).  See screenshot of editing Custom Form Styles (from the cog, top right).

And by clicking Show labels and widths you can change the template column widths a bit.

Our logo appears as well, I noted that some people says theirs did not.

Maybe not what you all need, but maybe it helps someone.

I haven't read this whole thread so apologies if this is discussed/obvious/unhelpful!