After a bit of work I got this functioning properly in 3.4.10. It should be noted that the additions need to be made to several more .tpl files. Namely those files that call out the shipping address in email notifications.
Essentially, the mod is thus;
Add the two columns into the database and then add b_address2 and s_address2 throughout the site.
Not a quick task but a good extended search tool will help you find s_address and b_address throughout your code. From there you just copy and add the '2' for address line 2.
Thanks much for your work on this and for your detailed explanation rodenyw!