When you use a quotative-と, the "quote" will basically be a normal non-polite sentence. That is, you can safely use は inside the quote, and you should not drop だ. Brackets are usually not used in a simple case like this. Therefore, the correct sentence is:
The polite version is:
As you may already know, 私は is normally ...
Assuming you already know the basics, here are the relevant rules you may be missing:
が is normally used to mark subjects in subordinate clauses.
But は is still used in subordinate clauses when contrastive meaning is important.
Both contrastive-は and exhaustive-listing-が "emphasize" something before it, but in different ways.
Therefore, 私が死んだら is the ...
Good question! This question is an actually an entire topic. For example, see this article.
So we have four patterns here:
The short answer is that they are all correct grammatically. However, they have slightly different nuances.
"は" is called the topic particle for good reason; it marks what ...