It will be a tough slog to weather and will take some dead time waiting for a weather window.
I lived in Newport Beach for a while and a local delivery captain wrote a weekly column about boating. He said that he would not take a boat less than 40' around Pt Conception (just north of Santa Barbara). He said it could be done, but it wasn't worth his time or the customers time for him to wait for a decent weather window. You are better off shipping the boat.
Also the number of bail out harbors are limited going up the coast. Again he said that it could be done but it depends on good planning, a sea worthy boat and a competent captain.
To your last question, I am sure that almost all skippers who take their boat south on the Atlantic ICW also take them back north. I have done it several times. In the early spring going north you often can't go offshore (in a medium size sailboat due to headwinds) so have to stick to the ditch.
There are delivery skippers who will take your boat over to the Bahamas and maybe even to the Caribbean and then back home when you are done. But I can't afford that.
David