It's not for the sake of veracity
Whether the historical Caesar pronounced or not the said words is disputed. Of five Antique sources on Caesar's death:
Nicolaus of Damascus, Plutarch and Appian do not report the quote
Suetonius and later Cassius Dio report it only as a dubious variant to the tradition, but using Ancient Greek rather than Latin: Και συ ...
It is left open by the playwright
I am going to look at the three characters you have chosen, starting with Cassius.
Cassius is not an honorable man no matter whether you think Caesar should have died or not. Here is a quote of him trying to use his power to free a friend.
That you have wrong'd me doth appear in this:
You have condemn'd and noted ...
As asked, the question is close to unanswerable. Specifically, your main question is:
What is the evidence - either from the text of the play itself, or from surrounding evidence, if any - of which of these interpretations the writer himself intended?
Gauging authorial intent from the text itself is a fool's game. After all, you've noted that different ...
Some of Shakespeare's plays were printed individually in quarto editions during Shakespeare's lifetime, but Julius Caesar is one of the plays that was first printed after Shakespeare's death in the so-called First Folio of 1623. As a consequence, the First Folio text of Julius Caesar is the only authoritative text of the play, and any variations you see are ...
I would paraphrase "rash humour" as irascible temper or fickle temper. Based on what Brutus said earlier, Cassius does not so much have a persisting angry mood; his character is better described as choleric (emphasis mine):
O Cassius, you are yoked with a lamb
That carries anger as the flint bears fire;
Who, much enforced, shows a hasty spark,