Yeah man, this is exactly what you need. Running orders through your own Amazon account is just asking for suspension. These third-party services act as a middleman they use their established Amazon accounts to place orders for your customers, then push the tracking back to eBay automatically. It keeps your personal account clean and scales way better. Reliable fulfillment for Amazon and eBay orders is exactly what this platform does, check out their FBE service here
https://easync.io/fbe/ .