If I follow you, the one door is code compliant for this job.
You have a layout showing two (2) doors, and the second egress is via a fixed ladder.
As the one door seems to satisfy code, the second door is a moot issue.
Now, as I said above....the physical layout and dimensions of the room and the gear IMHO is required to provide a definite answer that one door is compliant.
IMHO, IF the second egress is required based on the layout, then the fixed ladder will be questionable.
The purpose and intent of the egress paths and the panic style hardware is to get out of harms way if someone is injured, and the ladder could be an insurmountable obstacle in the egress path.