There is a process for extension for deployed military, but that is the only exception I have found.  You do get a 15 day grace period, but after that you may be SOL, and have to pay fee for new tags rather than renewal.  If you have your car with you, you may be able to get an inspection in CA since they require then also... just a thought, but would recommend calling NCDOT, to inquire either way.  877-368-4968

I thought you could get your car inspected at an out of state inspection place. They just have to perform the tests NC requires.  

I don't blame you for wanting to stay in SF for awhile. I was just there this past Dec. and wish I had more time.
 

happen before.  In the militart I could get a local inspection until I got back into my official residence state

From NC DOT website:  
15. My vehicle is due for inspection, but I will be out of the state. What do I do?
A person who is out of state may obtain an emissions inspection in the jurisdiction
where the vehicle is located in lieu of an inspection in North Carolina as long as it meets
the requirements of the U.S. Environmental Protection Agency (40 C.F.R 51).

FOR QUESTIONS ABOUT THE
NORTH CAROLINA INSPECTION PROGRAM,
CALL 877-421-0020

Now that you've got the exact answer for your dilemma, might I suggest that you find an inspection garage up in Sausalito, enjoy coffee and brunch overlooking the bay while your car is inspected, then drive on up to Muir Woods and indulge your wanderlust. I strongly recommend taking a water bottle, getting a map at the park office, getting  off the boardwalk and go walkabout and wind your way back into the grove at sunset. A truly spiritual experience, I promise.    I cant wait for your wandering to lead you back to Asheville so you fill my head with tales of your adventure, Sheherezade.  I peeked at your blog and the adventure is looking good (on you), indeed.

Don’t about NC but in GA it $25.