I wonder what would have happened if Spock DIDN'T die- he already put his Katra into McCoy for safe keeping. If he survived the repair job, who would be the real one since McCoy/Spock downloaded the Katra into the blank Genesis Spock and he was restored body and soul.
Was that Katra a complete copy like you back up your C: drive and if it was not needed you simply erase it? If not and it was an actual transference was the repair completed by a soul-less shell Spock?
Katra probably doesn't flee the body until the host is dead. Spock was just telling his Katra where to go when he ceased to be.
Surely radiation suits of this time period are specifically designed to be put on in a hurry, wouldn't you think? Just like hospital greens are today. They're made so a doctor can put one on lickety-split and not have to waste time fiddling with it.