SVWeb

Do the same as you do now but do it every three months. Can't really see the problem.

There is not much you can do with the iframe itself (other than style it in your style sheet of course) but there is nothing stopping you from wrapping the iframe around your own custom html.

As your client wants to use Revue for the newsletter creation there is no alternative.
You could pay a developer to fix it for you - might cost the client £100 (ish)
Or you could look at different newsletter creators and see if the have a plugin.
A car club I belong to does everything in mailchimp, I built a simple sign up form that adds names and email to the mailchimp list.
Or you can investigate one of these (there are many others):
https://winningwp.com/best-newsletter-plugins-for-wordpress/