I believe some of the BMA250 register address' you are using are incorrect based on the datasheet.
Register BMA250_RANGE should be 0x0F
Register BMA250_BW should be 0x10
The datasheet eludes to the BW setting as not just a lower update rate (2 x BW) but it may imply low pass filtering. I will need to perform more experimentation to verify.
I have not put the TinyDuino to sleep yet but will want to some time in the future. Please post what you come up with if you get back into this project.