If I stun a unit to prevent damage once in a showdown, do we commence combat a second time without healing taking place in between calculating total might? Example: 5 might, counterstrike proc, into 8 might, I assume takes 5, and triggering a second round of damage calculation, 5 into 3?

No, a second round of combat does not occur.

According to RiftJudge FAQ #6276, if units from both players remain at the end of a showdown (such as when a unit is stunned and survives), another showdown does not start. Instead, the attackers are simply recalled back to their base.

Why this happens:

1. Combat is not iterative: Combat damage is dealt exactly once during the "Combat Damage Step" (Rule 460.1). There is no mechanic that allows combat to "repeat" or "re-trigger" just because a unit was stunned or survived damage.
2. Stun mechanics: As specified in Rule 423.1.b and 423.1.c, a stunned unit does not contribute its Might to damage in the combat damage step, but it still requires full lethal damage to be destroyed.
3. Outcome: Because the stunned unit does not contribute Might, it deals 0 damage to the opponent. However, if the opposing unit fails to deal damage equal to or greater than the stunned unit's full Might, the stunned unit survives. Once the damage is resolved and the units are still on the board, the combat concludes, and the attacker is recalled to base.

Your example scenario—where you stun a unit and expect a second, separate round of damage calculation—is not supported by the rules. The combat resolves in one single damage-dealing step, regardless of whether a unit is stunned.