I went ahead and added the missing div. I had to do the same for plugin/user/sendy/sendy.xml and plugin/system/sendy/sendy.xml, so you might want to update all three.
I also used the sendy docs to create my own newsletter signup form using RSForms. This allows me to add the name field to pass to the Sendy database. Everything appears to be working properly. Thanks again for your help.