"Send to Email" address populated dynamically from custom_field

That post does exactly what you described. It populates an email field on the form with a custom field value from the post the form is being submitted from. That email field is then used for the Send To on the User Notification. The example in that post does work.

If you need it to show up in the "Send to Email" drop down you would need to use an Email field, not a Single Text field. Only Email fields appear in the Email selection drop down in the Notifications.

You are using the "Allow field to be populated dynamically" area wrong. That is for populating the field dynamically using custom PHP and via the query string. The parameter name you enter there is for then populating the field using custom PHP.

The post you linked to discusses populating the field using a merge tag in the Default Value for that field.

You would place:

{custom_field:user_email}

In the Default Value for this field. You would then set the field visibility to Admin Only so the user doesn't see it. In order for this to work the custom field key needs to be 100% correct and it is case sensitive. So if the key is user_email then my example above should work.