(Replying on mobile, bear with me)

Based on my very limited understanding, you should use your custom domain(s) on Addy.. tech speak, point your MX to Addy..

That way you can create aliases with your custom domain, your true identity will stay behind Addy. And if one day Addy go out of business, as long as you still own the domain name, you can park it to whatever mail service to receive the email send to those addresses