Hi. :) I am going to be really mean. It is not your fault that is just who I am. I am not trying to be discouraging. I think it is great you are asking for feedback. I know I have made some less than perfect things and I know I learned a lot from people who were less than nice. I do see real potential in you. I am going to be mean.
Huge missed opportunity by not having someone you need to rescue be in the location. If you told me there was a lost dog in the mouth of a dragon I would go into the dragon's mouth. As of right now the motive to enter the labyrinth is nonexistent and the reward for escaping is nothing. The sick player could be the person you went to rescue. The example adventure does not actually have much to do with the theme out to lunch and I think it is because your realized that is really boring. It is literally saying "that thing you came here to do no you can't do it because I said so". I know what you are trying to do. This is the lotus eaters den or Noradz. The problem is the delay in arriving and noticing something is wrong. There is a period of time where you just have to wait for something to happen so you can react to it.
I want to compare it to Noradz again because it is the first thing I thought of. Noradz is weird. The heroes arrive looking for something and can not leave until they find it. The people keep repeating the phrase "Clean Noradzs here" and brushing their shoulders. They refuse to explain why. Any mess no matter how small is always punished. Their town was destroyed by rats. Noradz is a combination of the words no and rats. The entire town is obsessed with keeping rats away. In Noradz if you try to do something someone will try to stop you because it may attract rats. In your game if you try to do something you can't because the person you are looking for is either out to lunch or useless. If they do try to do things right they get rejected for using the wrong color ink. Only after something the GM decides happens can you react to that thing and maybe get into a fight. Noradz presents a problem to solve. Out to lunch presents a problem you have to wait for the GM to solve.
One more example. Bait location number three: A never-ending athletic tournament with all manner of martial and physical challenge available. How is failing to do paperwork more interesting and fun than doing the tournament? I you promised me a tournament and I got "this is the wrong color ink" I would never play with you again. If there was actually a tournament I would not be charmed by the never ending impossible paper work I would be annoyed by having to find a guy who is not at his desk because I could be doing tournament stuff right now.
I like the writing. The example adventure was fun to read, but I don't think it would be fun to play. Not unless it was twenty minutes. Your projection of two to four hours is way to long. I know this is not an adventure it is a framework but it feels empty. It boils down to "Have you considered there might be something sketch going on at that tournament? What if someone was dragged through a door and no one closed it?" If I was going to run an adventure in Noradz I would not use this as a framework. Step three [The Bureaucracy] is exploration in a (not so) funny hat but you don't provide anything to explore. If I had to guess your Wild Sea adventure was fun not because of the bureaucracy but because you were playing Wild Sea. Just a guess. You missed the forest for the trees.
Final thoughts. This is over written. It is too big. Instead of trying to be everything to everyone it should have been one specific thing. I find this frustrating because I see what you are going for. This could have been great. Despite the fact I think this misses the mark, I don't doubt your next project will be great.