an easier way to do this is to have one spawner set up to do sequential spawning and configured to trigger on speech. Put your successive spawns into successive subgroups on the one spawner instead on multiple spawners.
To allow it to be triggered once and then run on its own until it reaches the boss without additional triggering, have it configured to set FreeRun on itself to true when it starts. This will allow it to continue running just like a regular non-triggered spawner until you set FreeRun to false again at which point it will wait for triggering again. For example
Subgroup 1: SETONTHIS/freerun/true
Subgroup 2: orc
...
Subgroup 8: bossmob
Subgroup 9: gold,10000
Subgroup 10: SETONTHIS/freerun/false
Subgroup 10: GOTO/1
If you also want it to automatically reset to the freerun=false state if they dont finish the sequential spawn, just set the ResetTo field to subgroup 10. That way, if they dont finish a level it will turn off freerun and go back to the initial subgroup 1 and wait for triggering.

(edit)
erm, on rereading your post I think that I misread it the first time.
I gather that you already have the sequential spawning thing going, but that you want to have 3 sequential spawners like that running at the same time, but when you do the Dorespawn thing, it clears the exttrigstate that you just set.
ExtTrigState does get cleared whenever the spawner is stopped. That occurs when you reset or if you SET/running/false. I dont believe that it should happen when you respawn, but I would have to double check that.