There is no powerful subscription management service for Joomla and maybe Wordpress that can deal with subscription services with the reliability a large user base needs.
We use one now that is a saas integrated into Joomla and it works OK, not great but far better than any standalone system.
I use your invoicing system and see how the full features of the subscription manager would work very well ....
... if a pre-written API that is supported by you were available to make passing details of plans, current status of a subscriber and a way for the subscriber to update their info directly existed. I have two sites that would be immediate users if it works as well as it looks like it could.
And there are thousands of sites trying to make subscriptions work in these two platforms. None I've ever found did what they should.
It's your opportunity....