1. All of the CA schools ask for the LOR at the time you send in your secondary. Some actually state vehemently to not send in the LOR before asked to do so.
2. 6 LOR might be too many for some schools. I am a non traditional app (29) and so felt that I had to have letters from my various activities over the years (undergrad, grad, work, etc.). But, I was limitted by some schools who asked that no more than 4 or 5 be sent in.
3. There were several schools that had particularly specific requests regarding LOR. For instance, USC required that you have two from your undergrad institution (not a problem for many, but I was only planning on one because it had been 6 years since I had attended there), others want the recommmender to fill out a little waiver form that you have signed, etc. All in all, I would have the letters lined up and waiting (in your premed office, etc.), but wait until each school requests them so that you can meet their individual requests.