Call the Gerlach post office. General Delivery *should* work. If you're staying in a hotel in Reno before going to the playa that's another option.
People do get packages on playa through the post office, but I don't know when they start delivery and I think there's a certain burny randomness that you may not want to rely on. Can you have it delivered to your friend at his/her home address? Perhaps you could rent a mailbox at one of those mailbox places. I'm sure there are other options, I think this is a brain storm and then look at the pluses and minuses situation, rather than having a perfect answer on a platter. You are going to have to weigh security, price, and other factors, and only you can decide what each is worht.
Edited to add: You might be able to work with Artery on a solution. It's possible they've done this before.
Lose your legs--Become a merit badge.
I'm a passionate, childlike innovator.