You can achieve step 3. by using an auto-relation.
Instead of using the Assignment extension, create a relationship between the Issue type and the User type, and set it to automatically link when the value of the Issue field used for email (added by Zapier) matches the email field for the User.
The disadvantage of this is that these sort of relationships to Users don’t provide the notification functionality that the Assignment extension does, but if you can live with that, it gets you what you wanted.
Hopefully, a more developed notification functionality won’t be too long coming
See here and here and here.