Having updated to 6.3.2 of the plugin, I'm still getting the 404 error as clicking Settings tries to load mysite.com/wp-admin/options-general.php?page=ga_activate.
I realized that the URL above isn't correct, as my site's WordPress installation is in a subfolder of the www directory. When I added the sub-directory, I was able to get to the activation page and input the code.
However, on clicking Save & Continue I get the 404 error again as the URL doesn't include the subfolder. Adding the subfolder to the URL at this step doesn't work, so I'm still unable to activate the plugin.