Honestly, here that would never fly. You may be able to work something out, but for some schools not only would you get a "no" but they would wish they had not made an offer to someone who did not want to commit. In complete seriousness, any discussion of this during an interview would absolutely kill your chances of a job. Your school and situation may be different, but tread very carefully. On a more general note, if you only want to be tt part-time, you probably need to get out of the tt business all together and find a part-time position that will allow you to do other things.
This is exactly my school too. You start asking for a delayed start and we get nervous. We have nightmares of having the hard-fought tenure line being pulled out from us. We also wonder if this just a convenience job for you.
Except for truly compelling medical or family issues, asking for this here is just bad news.