If I attack with a Glasc Mixologist and it dies, can I play a unit from the discard into the same battlefield attacking before the showdown ends?

No, you cannot play a unit from your trash to that battlefield because you are the attacker and do not control that battlefield during combat.

The Ruling

According to FAQ #9479 and FAQ #9314, when you move a unit to an opponent-controlled battlefield to attempt to conquer it, you are the attacker and you do not control that battlefield. You only establish control after the showdown is resolved and the battlefield is successfully conquered. Because you do not control the battlefield, you lack the permission to play units there via Deathknell.

Sequence of Events

1. Combat Damage: You attack with Glasc Mixologist into an opponent-controlled battlefield. Damage is dealt, and Glasc Mixologist dies.
2. Deathknell Trigger: The Deathknell ability triggers and is placed on the chain as a pending item.
3. Resolution Attempt: You attempt to resolve the Deathknell ability. You are instructed to play a unit from your trash. Because you do not control the battlefield where the combat is taking place, you are not permitted to play a unit to that location.

Why this is different for defenders

As noted in FAQ #9149 and FAQ #9541, a defending player is permitted to play units to the battlefield using Deathknell because they already control that battlefield when the combat begins. As an attacker, you must successfully conquer the battlefield to gain control of it; until that point, you cannot play units to that location.