If you are getting a 20% open rate but no good conversions then I would suggest it is the content within the email that's not working. The strong open rate means your subject line and general trustworthiness as a sender is not a problem, but your content just isn't hitting the right angle.

Based on what you've said about the content of your emails it seems to me like they are all quite price-led messages (offers, coupons etc) but maybe that's not the best way to go. Maybe you need to find another angle or a set of angles that will convert better.

These customers haven't signed up straight away so that means they must have unanswered questions about your service that's preventing them from making a decision. What are these questions? Find out and build a content stray around this.

Or maybe go for a softer content-based approach rather than going straight in with pricing offers. Build credibility first over a longer series of emails and keep the pricing emails to a select few throughout the series.

Hope this helps.