I'm curious as to why you used 2k2 resistors and not values that have convenient doubles (eg 10k & 20k or 1k and 2k even) and save yourself a load of parts and work. The accuracy thing with modern components is no better if you use the same values or mix and match the convenient doubles.
If you lose the bet though and do actually get a 1% resistor value error then potentially the bottom two bits of your 8 become meaningless and would probably just make your sinewave look a bit fuzzy.
Thanks for sharing this as well. If I want to use the Due DACs this kind of information from you and the replies from others can be pure gold!
PE.