If it were me, I would try and get the Madone close (at least you should be able to pull the seat height and fore/aft off your old bike). That way you can ride it and be ready when the fitter dials you in. I'm assuming the Madone will be your main bike, so makes sense to fit you on that.

Also depends on how the fitter fits you, fit kit, Compu-trainer, experience, etc... To get the best fit you really should be on the bike you'll be riding. Stems, reach, bars, are the last adjustment usually made (assuming the bike is the correct size), so you can dial in whatever you like. While a lower position will likely me more aero, a slight rise may make you more comfortable and efficient - thus faster. Depends on type of riding and style.

Enjoy the bike, Kim has so much studying to do, she wouldn't have time to ride even if her bike did show up early.