Resolving Multiple Demise Abilities

[King of Draconis]

My question is if a model has two demise abilities, one of which keeps it alive, can the other one still work? If so, does the order matter?
My only example so far is putting a Two Gremlins in a Ghillie suit on Bad Juju in a Bayou Zoraida crew.
If Juju is killed, can the player discard a card and save Juju AND summon a Bayou Gremlin too? If the player starts with discarding, then the model is not killed anymore, so the "I'm Done With This" will not be triggered imo. But what if the Gremlin gets summoned first, can the Zoraida player still discard a card instead and save the henchman?

Update: I've found another one: Freikorps crew with Deso Engine in it. As a minion it can get a Land Mines Upgrade. Gets killed, replaces with an Abomination (loses the upgrade, as during a replace it does so). But can the DE still use the Mines' Demise (Explosive)?

Edited January 5 by King of Draconis
another example came up

[Mortarion]

Any effect which heals a killed model will happen first, and therefore cancel the other demise ability since the model is no longer being killed.

From page 25 in the rulebook:

"When a model is killed, any Healing effects or effects that result in the killed model being Replaced happen first, followed by any other effects that occur when, if, or after the model is killed."