We've been in that situation 5 years ago. Stripe's customer service moved the data (customers, subscriptions) over for us.
Edit: I've been corrected by my collage. Stripe only copied customer records. We had to manually stop and recreate the subscriptions.
Exactly, that is the only part automated by Stripe.
I have never done this personally, so no real experience, but I would try to handle everything but customers by using Terraform.
*colleague