ANB, welcome to eplaya. Please tell us that you have read the survival guide a bajillion times.
The suggestion to rent a suv and trailer is a good one. The camper rentals are getting harder to come by, plus they can cost a boat-load of money, especially if you return it all dusty and all.
You don't want to backpack into BRC unless you have joined a camp that is supplying infrastructure. You won't be able to carry everything that you need going solo. This isn't the AT.
Simons advice is good, another option is flying into Salt Lake City.
If your friends are getting squeamish now, imagine what they will be like when they get to the playa, squeamish on steroids. You may end up dis-friendling them, do you want that on your conscious?
Excuse me Ma'am, your going to feel a small prick.
Algorithms never survive the first thirty seconds of patient contact