Could cook them separately - the extra energy isn’t a big deal, assuming an insulated container with some kind of lid. But just throw it in at 65 or 70 if you want it all together (although you can add the breast after an hour and then take it all out together). Breast at 70 will still be completely fine/significantly better than when most people roast chickens!
If you ever want to do a whole chicken a fun/interesting way, look up the Pepin ballotine/galantine video. Basically debones a whole chicken so you can stuff it, tie it, and cook it... then you can take delicious slices and put in sandwiches/chop sections and add to whatever you make/etc. It’s a cool skill to learn/might make your prep more interesting if you’re in to learning stuff like that.