Migrate old subscriptions to stripe
Solution 1:
I believe you can create a Subscription with a trial period. Ie. If your customer purchased your services 3 months back, you can create a Subscription with trial period = 9 months, or even 1 year if you don't mind giving them 3 months free until today + 365 days.
When a subscription is created with a trial period, it won't ask for a Payment Method. When its billing cycle is approaching, Stripe will send a trial_will_end webhook event for you to start collecting your customer payment method.
There is also a Stripe's official doc for trial Subscription.