I think it's worthwhile to take a mathematical look at the tea tasting. Let us start with these assumptions:
1. There were 1500 cups of tea.
2. There were a very limited number of cups that matched the reference sample tasted in Kunming.
3. For every 5 cups sampled, an individual went to the tea master.
4. Some individuals used their sense of taste or smell to "beat the odds" and others did not; for the latter this became a needle-in-a-haystack task.
Let's say there were 8 matching cups among the 1500 ( I tried it with 10 and the results did not reflect the real situation well). That means the odds of an individual tasting each cup without special knowledge would be 0.5333%. If we say that it took 15 seconds to choose and sample a cup and another 15 seconds to get the result verified, then here is the way it would have gone on average assuming no smell or taste assistance:
#1 8 cups available 94 tastings to reach midpoint in average 28 minutes
#2 7 cups available 107 tastings to reach midpoint in average 33 minutes
#3 6 cups available 125 tastings to reach midpoint in average 38 minutes
#4 5 cups available 150 tastings to reach midpoint in average 45 minutes
#5 4 cups available 187.5 tastings to reach midpoint in average 56 minutes
#6 3 cups available 250 tastings to reach midpoint in average 75 minutes
#7 2 cups available 375 tastings to reach midpoint in average 112 minutes (a bit less than the 3+ hours it took Flight Time)
#8 1 cup available 750 tastings to reach midpoint in average 225 minutes (3.75 hours, close to what it took Luke)
Teams using taste or smell to their advantage would have finished more quickly than indicated above, but the last 2 teams were in for a very difficult task.
That's a nice start. But just a little too simplistic for the computer age.
What you have not taken into account is that the number of cups is diminishing as the tasting goes on. This has a mathematical consequence that will help to reveal the real arrangement of teacups left out for the teams.
The main parameter at play is the number of "good" cups available to pick from. It does not have to be 8
I think 30 seconds is a better estimate of the time needed to select and drink each cup. Plus there is going to be some time used to run to the far end of the Hall to show the judge. I also upped the time needed to get checked by the judge: 30 seconds because, as we saw there was a bit of a queue. That 30 seconds is for 5 tastings as you did. I found that with 10 good cups out of the 1500 the teams could be expected to complete in the following times:
1st 13 min
2nd 25 min
3rd 40 min
4th 58 min
5th 79 min
6th 106 min
7th 147 min
8th 226 min
Running the same experiment with only 8 good cups produced the following expected completion times:
1st 16 min
2nd 32 min
3rd 74 min
4th 102 min
5th 79 min
6th 142 min
7th 204 min
8th 355 min
And finally, running the same experiment with 8 good cups and your 15 second tasting and judging times gives the following expected completion times:
1st 7 min
2nd 16 min
3rd 26 min
4th 37 min
5th 51 min
6th 71 min
7th 102 min
8th 177 min
You can see that the model is linear with the duration inputs.
So after making these runs I concluded that in order to be consistent with the 3 hours and 3.75 hours for the 7th and 8th teams we needed to have the Roadblock set up with 10 good cups of tea on the tables.
To Luke's credit I suspect one or more of the three good cups he was supposed to have were inadvertently tasted but not taken for judging.