Try doing it using my ATTinyCore, and the builtin Wire library (instead of TinyWireS) - my core has a builtin Wire library that automatically selects the best I2C implementation available for that hardware, and it should use the appropriate code to do I2C slave with the USI, and it should work. If it doesn't, that's something I need to fix (and a perfect test case, since you've been kind enough to give me code!)
If that doesn't work, post schematic as well as adapted code.