If you are charging a higher rate, part of the value associated with that is a certain degree of flexibility.
Also don't see the problem with the client wanting a cell number, if you don't want calls on your personal phone just get a cheap second phone + SIM for business. Make it clear which hours you will be available, put the phone on silent during family time and check voicemail periodically. I would be sceptical of giving somebody $20K who won't give me a "real" phone number.
I always find that speaking to somebody on the phone or in person regularly leads to a much better long term working relationship than simply email or IM. It's much easier to trust someone when you can associate them with a face or voice.