How would the following scenario play out:

Quickdraw is equipped with Elusiveness and Electronic Baffle.

An enemy ship fires at Quickdraw. During the modify attack dice step, Quickdraw uses Elusiveness and takes a stress to force the attacking ship reroll one dice. However Quickdraw Baffles off the stress taking a damage in the process, losing a shield, and activating his ability.

A) Does Quickdraw’s ensuing attack “interrupt” the current attack? (And then once finished Quickdraw would roll defense for the original attack).

Or

B) Does the current attack finish completely and then Quickdraws ability goes off?

In the event of A, what if Quickdraw kills his attacker? The first attack just fizzles and ends during the modify attack dice step?

Quickdraw does not interrupt the attack at the moment of losing the shield, but triggers after the initial attack has been resolved but before any destroyed ships are removed.

From p.14 of the current FAQ (4.4.1)

That means, as @Parravon said, after the incoming attack deals damage, but before any ships are removed.