Put the first script in the Shutdown Items folder. The last thing it should do is tell the next script to run:
ignoring application responses
tell application "nextScript" to run
end ignoring
The other scripts won’t be in the Shutdown Items folder. Each succeeding script will launch the next one. You must not let any intervening applications get brought to the front as this will will interrupt the original shutdown. If the last script initiates another shutdown it will put you into an infinite loop unless you make special arrangements to avoid it, such as setting a property in the first script to ignore the next time it’s run, i.e. it will do its thing only on every other exection.