Hi there, this is Marc. Thanks for reaching out the community.
If resetting is putting you in a loop, the best approach is to go through the Microsoft account recovery process instead of just the Skype page. You can try: Go to the official recovery page: https://account.live.com/password/reset and follow the prompts.
If you no longer have access to the old recovery methods, submit the Account Recovery Form (ACSR) here: https://account.live.com/acsr. Make sure to use the email/phone linked to your Skype ID and provide as much information as possible.
Regarding linking your paid Skype subscription or balance to another email ID, this unfortunately isn’t possible. Paid Skype accounts and balances are permanently tied to the original Microsoft account. To continue using your subscription, you’ll need to regain access to the original account.
Best regards,