My first choice to solve this problem quickly would be to use an enterprise label print server like Loftware or Bartender. But, like you said, they are expensive and you are planning on reselling your product.
My second choice would be to scrap the activex control and build a simple print server. There is no standard control language in the label printer world but if you are going to standardize on a certain class of Zebra printer you would only need to implement one driver at first. I have only ever done this for Datamax printers but I'm sure the process for Zebra printers is similar.
The server takes your label data as input (pallet ID, ship to address, etc), inserts that data into a template (painstakingly crafted in the text based printer control language) and then this label file is sent to the appropriate printer.
My third choice would be the browser based solution you are looking for. IT departments hate that stuff.