I don't have the times right at hand, but search Amtrak for SAC/SF and you will see the bus connections at EMY. As I recall there is one just less than an hour after the scheduled arrival of the CZ with about four others up to about 10pm. One issue with the LD trains is timing. CZ appears to have been on time, or close there to, the last few days, but you never know. The other variable is how long to retrieve your luggage from Amtrak.

However, if you've got four adults travelling, I would guess you'd be able to wrangle your luggage onto the train yourself without too much hassle. Boarding at CHI should have plenty of room in the luggage racks just inside the door. The advantage here is you will have access in case you want something during the trip.