This is something that companies that are near public company size do since the amount of work required to meet payment regulations alone, not to mention all of the infrastructure to support things like subscriptions is staggering.

This is why there aren't many solutions to this problem. It's a very difficult problem.

It provides a subscription management platform with all the features you would expect out of the box (recurring billing, plans management, dunning, notifications, etc.), but with also a plugin framework where you can implement your own billing logic.

You can continue to use processors like Stripe to handle the recurring charges (and compliance associated with storing cards), but they are only used to charge the payment methods. The mess that OP mentions stays in-house, where you have tighter control over it.

[1] https://killbill.io/