Eyuh. However, I think you're approval's well on its way and in my opinion it should be around the corner, so I think the bar ball's in your court.
Fax: Yes, there USED to be a published fax number for the TSC to request expeditious case processing. All other faxes were summarily ignored. Ditto for the other service centers. Unfortunately, they don't publish this number anymore, and refer and expedite cases to the National Service Center's 800 number (and we all love speaking with those folks).
Anyway, if you don't mind me asking...why're you trying to reach the TSC? Is it to prod your case along? Your case was sent to the Lincoln for an interview, right? Regardless, none of my business, but this is what I highly recommend. Don't waste your energies trying to contact the service center yourself. You need a person in the semblance of some power to undertake this otherwise monumental task for you. What I did was contact my congressperson and her director of constituent services has been highly proactive in exchanging email with the TSC's Congressional Services Liaison. Which proves that the TSC has such an entity within its fold, so leverage that. Odds are high that any letters from applicants are ignored. Trust me....my letter to the VSC back in Christmas yielded absolutely nothing. At Christmas nonetheless....way for some Holiday spirit.
Anyway...you're in Cali, so given the hot debate over (illegal) immigration, your congresspersons might be more than willing to help. Barbara Boxer? Is that right? Find out what jurisdiction you fall under and contact the congressperson. Explain that you're name check is done, your PD is current, and whatever else you need to contact the TSC for and have them call. It might take a couple of days, but you're at least assured a response rather than have your letter languish in the obfuscated obscurity.