"The essence of self" seems like the wrong question to me. That sounds too much like "What is the essence of your personality?" and that's irrelevant here.

What I'm talking about is my ability to experience. We all have an ability to experience (I assume) that, although it may be shaped by our personalities, it is not our personalities. Example:

A Christian sees a Satanic ritual. A Satanist sees the same ritual.

The Christian is horrified. The Satanist thinks it's great.

The reason one was horrified and the other thought it was great is because they have different beliefs, possibly different personality types, different life experiences and possibly even different neurological wiring.

What did they have in common?

They both saw a Satanic ritual.

THAT is the part I am trying to point out here. The part that experiences. It's not one's personality, or beliefs, or experiences or neurological traits.

I am saying essentially "Even if personality, beliefs, experiences and neurological differences are copied, this does nothing to guarantee that the part of you that experiences is going to survive." Asking to define the essence of self is not relevant since I'm saying to you "Even if self is copied, this thing that I am talking about may not survive".

Here is a clarifying example:

Transporter Malfunction Scenario