- I thought that using pullups to 3.3V (instead of 5V) were enough to make this work, as can be seen in the attached schematic.
This is a correct assumption in most cases.
- About the 2K7 resistor: I started out with a 5.xK resistor, with the same results. In the datasheet it said to use 1K resistors... So if I just use higher value resistors, will I damage the chip?
1k is the absolute minimum resistor value for a 3V system (according to the I2C specification), so it's too small for a 3V3. Although most devices probably work under such circumstances you cannot really expect it.
Are your values correct? Have you checked that? If you you probably can just ignore the status value of diagnostic condition.