Try to set Lux or Science above 50% in Chiefdom, and you'll see it isn't possible. But, as Greebley explained, if you turn both down, Tax will exceed the 50%.
The AI cannot do that; they will always stick to the rules. This was a DyP feature since ever, so we know it pretty well.
The bug is that the game checks for the cap after commerce is distributed, and resets it too late.
'Respect the Rate Cap' is a houserulle for my games.
And, it doesn't really give you much gp anyway if you only turn it down the last turn before a tech is researched. How big is our total income, 10got?
Oh, and I would be careful with burning too much cash. Due to all the (necessary) city improvements, maintenance will go up pretty soon. Add the unit support, and we can be in trouble soon. I'm currently playing an RaR AWE, and I cannot afford more than 20-30% research for most of the time in Monarchy...
Useful upgrades like TGs to Spears is worth spending money, but upgrading many Slaves is not the best idea...better get more of them

.
Speaking about Govs: Republic, or Monarchy until we get Absolute Monarchy? Republic has the trade bonus, but WW will be pretty ugly...
And, there is one wonder we should get by all means: The Sphinx (Sun Tzu's equivalent).