Some of the AVRs have fairly decent 12-bit DACs. You could merely shift the zero using an op-amp. Say your DAC reference is 2.5V, then you could shift the output by an input-referred -1.25V so you get a bipolar output signal with output 0V at 0x800.
The general approach would be something like this:
simulate this circuit – Schematic created using CircuitLab
Just throw a bit of algebra at it- for example for Vref = 2.5V and desired output -4.0V to +4.0V you could pick Rf = 10.0K, then R1 = 6.25K and R2 = 16.67K.
The above circuit does not load the DAC output, but it does present some load to the Vref. If it's not very low impedance you could use another op-amp in a dual as a unity-gain buffer so Vref also is not loaded.
Of course your op-amp requires bipolar supplies or it won't give you a bipolar output.