Complex outside of combat interaction

I'm trying to figure out how to handle an involved outside of combat sequence.

The short story is I'm wondering if the part of the FAQ that mentions this that says "check for disruption and destruction" means to completion.  So if multiple pieces are marked for disruption/destruction do you resolve that until no more pieces need to be handled before handling any triggered abilities (i.e. Deathblast)?

Example I ran into:

Brighthammer Avenger is moved and Charge triggers
Brighthammer controller chooses a piece to attack, in this case a Hazardin Grenadier and does enough damage to destroy
Outside of combat damage is handled once Charge resolves (damage assigned and stack is empty)
The Grenadier has a granted 'Last Gasp' through a Halo ability (Boneclan Wardrummer from Scud-O's set)
Deathblow happens and enough damage is assigned to destroy the Brighthammer
The controller of the Brighthammer is the active player so they destroy the Grenadier which triggers the Deathblast.

And this is where I'm unsure what happens.  The outside of damage handing hasn't completely finished.  If it had, the Brighthammer would also be destroyed and wouldn't be able to be targetted by the Deathblast as it would be in the graveyard.

Does the triggered Deathblast interrupt the outside of combat damage handling?