Also, Spock was mentally fine (as well as can be given his irradiated condition) for the 5 or so minutes after he transferred his katra to McCoy, meaning the katra transfer basically copies his memories instead of cutting and pasting them onto McCoy (otherwise he would be like "Who are you guys? What am I doing in this chamber? How do I even know how to speak?")
It's not plausible he could have transferred everything in the scant seconds he was touching McCoy. Therefore he must have established a telepathic link that continued during that time. So it transferred at whatever rate is normal and once the body is dead the last bit jumps over all at once, which it can do only at the end when it no longer has the original host.