I did some more work on pressure sensor testing, this time with a MP3V5004 sensor which has higher accuracy than the MPX5010. This sensor definitely did work better than the MPX5010, but it still was not accurate enough for my purposes. I also leanred that my test rig was very sensitive to two things: 1) The position of the tubes (even if one of them moved 1/64th of an inch it would affect the readings significantly), and 2) if there was liquid already in the tube from a previous reading. To correct this I secured the rig's test tubes so they couldn't move at all and I made sure to clear any liquid out of the tubes between readings. With these changes I got much higher accuracy, but the sensors I tested were still not accurate enough.
I found another pressure sensor made by Honeywell (HSCSAAN001PDAA5) that has significantly higher accuracy, but it is also MUCH more expensive ($40-50 per sensor). So I'm going to try some other specific gravity measurement ideas before I invest money in the pricey new pressure sensor.
Lately I've been experimenting with counting CO2 bubbles produced by a fermentation as an indirect way of measuring specific gravity. Currently I'm using a method which shines an infrared beam through an air lock. When a certain amount of CO2 has been produced in the reaction chamber a CO2 bubble goes through the liquid contained in the air lock (which really just acts as a one-way valve). When this bubble escapes it breaks the infrared beam momentarily which I can then detect electronically.
So far I've proven that I can detect bubbles with this apparatus; now I need to make sure that I can detect close to 100% of the escaping bubbles. Here are some pictures of my current test setup: