Okay, so I'm gonna have a look at all the recruitments as a breakdown...
There, I've added a tab to the spreadsheet,
https://docs.google.com/spreadsheets/d/1pmolfTSogaebDJo_qDpkmUkpvmd5QPl9dtVo4wmoqZI/edit#gid=535831188 so everyone can see the numbers. In short:
There was definitely a significant shortage of peasants compared to average, and a glut of Merchants and Priests in it's place. Engineers were just slightly below average in representation.
Turns 8 onwards had actually a very close to average mix of cards, overall over the 5 turns. About the only way it could have been more average is if one of the Merchants was a Priest at some point. So most of the uneven weight happened before that point.
The peasant count was definitely way below average. Not once were all 4 peasants drawn, and in fact rarely were 3 peasants drawn - only once in the first half of the game. The biggest disparity as a percentage of the averagewas turn 7, by which point only 2/3rds of the average number of peasants had been drawn. From there, their draw rate was about average - it stayed at roughly -6 from the mean for the last few turns.
Perhaps less noticable due to it not causing such an issue was the overabundance of Merchants. Only once did a lone Merchant come out (the round that eHalc was talking about earlier), and both before and after that, an above average number of Merchants were drawn. I think this showed - not only were people passing up Merchants regularly, but people still had multiple camels left at the end of the game.
The Engineer count was pretty close to average throughout the game. Well, just below average, but over this many samples that's close enough to call average.
Priests went the other way to Engineers, and were mostly average for a bit... but then suddenly came out in huge numbers around the midgame. Three rounds with three priests in a row is kinda a lot.
Overall, the obvious deviation from the average was peasants and to a lesser degree merchants. A real shortage of peasants meant more time was spent fighting for those Tammouz actions, I noticed, and the peasants all went quickly.