Edit: I'm gonna stop doing this because I didn't realize it impacts the "Not Dying" bounty.
Bumping So you know to NOT DO THIS:
Excerpt from OP:
When I grind ROC strikes and I'm doing the Archon Priest strike, every time I get to the "Think they'd mind if we take their pikes?" part, I try to go straight to the strike-boss "arena" as fast as possible, bypassing all the adds along the way.
Frequently, I'm able to reach the zone where the respawns disable before my two teammates appear on the radar. If I can pull this off, I head straight for the edge of the arena and jump off. This triggers a wipe, since I'm the only one who's "registered" in the no-respawn zone.
Thanks for clarifying about this, wasn't aware of how the mechanic worked. TIL!
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Do it all the time. If they don't want to die, they should do normal strikes.