Thanks for all of your input.
Mike, it appears that your suggestion is the most practical one, although it may cost a little bit to do. Ultimately, though, it will pay off in the end.
Thanks for the other suggestions, guys, however as Mike pointed out, at least 80% of our orders involve a mix-n-match situation, and as different lines and varieties have different prices, creating a “Case of 12 bottles” product for each configuration would be almost impossible.
I have been dealing with a local WordPress/Woocommerce specialist in our region, though, and he is working on creating a plugin extension for this issue.
Thanks again for your input though.