It turns out my accelerometer wasn't dead to begin with. The ESP8266 just hates SPI devices. The new accelerometer arrived in the mail, when I hooked it up via SPI it still didn't work. Then I tried both through I2C and they both work! I already ordered a Wemos D1 Mini and checked the SPI wiring with it and it doesn't like it either, and again the I2C method works. I checked again with my Arduino Pro Mini to make sure I wasn't crazy and the SPI method does work with it, just not the ESP8266s.
So now I am left with the same problem again, how do I get both the TCS34725 and the LIS3DH to work wirelessly? I thought of a few things:
If you are looking for a summary for my Masters thesis, it is here.