How can I make my yeast experiment more chemistry-oriented?
It sounds like a perfect chemistry experiment to me. It sounds good enough to even be one of my AP chemistry labs. As an objective for the lab, you could try to determine the amount of CO$_2$ gas produced per amount of sugar you use, (with all other ingredients in excess). I'm pretty sure the equation for fermentation is C$_6$H$_{12}$O$_6$ → 2 C$_2$H$_5$OH + 2 CO$_2$ (although note that common granulated sugar has the equation C$_{12}$H$_{22}$O$_{11}$ and decays into two glucose molecules when combined with water).Why not test a certain amount of sugar (like .1 moles) and see if you yield the theoretical .2 moles of CO2. You could use the ideal gas laws (PV=nRT) to determine the moles of CO2 product you yielded. Compare what you yielded to the theoretical amount you should've yielded. If you yield less, then you could include in your report/conclusion including why you think your yield was short.

The lab would involve gas laws, chemical equations, and percent yield, all of which are chemistry topics/principles. What is your current level of chemistry experience? If you haven't learned of anything I mentioned, I can help explain it better and point you in the right direction if you'd like.