The people at my favorite (please don't ask; I have a horrible track record in choosing apartments) moving company, Delancey Street Movers, firmly recommend (require?) that one pay the city to put up temporary "no parking" signs at both ends of the move; they claim that the ticket for a double-parked moving truck can cost up to $700. Having my stuff moved by Delancey is always an emasculating experience (choice quote from this page: "The average resident [of the program] has been a hard-core drug and alcohol abuser, has been in prison, is unskilled, functionally illiterate, and has a personal history of violence and generations of poverty."). I'd rather not also appear to be unable to follow instructions to secure a parking permit.
I first called the DPT number that I received from Delancey, 415-554-9928, but I gave up after remaining on hold for fifteen minutes. Some searching on the web brought me to this aging Yelp thread. As is often the case after visits to the site, I was left feeling not particularly wiser than before. I didn't find any relevant information on the SFMTA's site either, so I tried calling several other city phone numbers. 415-614-3405 is the number for the Northern Station's permit officer; upon calling, I was redirected to 415-614-3427, the station's "no parking request line". That number yielded a recording stating that the fee for up to four signs in one spot is $153.57, and that residents moving from the district to another location in the city can pay $202.16 for a double posting. I left a message after the recording but never received a call back.
I was curious about whether the Mission Station offered a similar discount for a double posting, so I stopped by the next morning to ask. My consistent experience has been that one will need to wait at least ten minutes if someone else is already being helped at the counter in the station, so don't go if you're impatient or in a hurry. When a second window was eventually opened and I was called forward, I was given this form and told that I would need to go to the Northern Station to arrange for the posting at the move's destination. The woman that I spoke with also gave me the phone number 415-558-5457 for an Officer Dempsky. Perhaps calling him or her immediately would've saved me some trouble.
I next visited the Northern Station, where I was given this form and told essentially the same thing: I would need to coordinate separately with (and pay separately) each district's police station. Note also the different rates quoted ($153.57 per the Mission Station's form and the Northern Station's phone recording vs. a handwritten $159.72 on the Northern Station's form) — either the Mission officers are lagging behind in updating their fees or the Northern Station officers are taking home a bit extra.
After considering my options over the weekend, I eventually decided that I'd go ahead and pay the $313.29 to get signs at both ends of the move. I went to my bank and took out two cashiers checks. I dropped off the first one along with the completed form at the Mission Station and then biked up to the Northern Station, where Officer Murphy politely inquired as to whether I was aware that I could pay just $210.26 to get signs at both ends of the move. She handed me off to Officer M. Lobre, who suggested that I return to the Mission Station with a check for the difference ($210.26 - $153.57 = $56.69) and ask them to post both signs.
Foreseeing exactly how that would go, I suggested that I instead visit my bank right then for another check and pay the difference ($210.26 - $159.72 = $50.54) to the helpful-at-least-for-the-moment folks at the Northern Station, and then cancel the request at the Mission Station. And then that's what I did, with the expected hurdles (apparently the only person who can cancel no-parking requests was out the first time I returned to Mission Station, so I had to come back again later). But now I've paid a total of "only" $210.26 and am at least partially under the belief that signs may appear at both ends of my move.
The depressing morals of the story (at least thus far) seem to be that the only thing worse than attempting to work with a bureaucracy is attempting to work simultaneously with multiple bureaucracies; and that sometimes your questions will get answered by people who don't know what they're talking about, and your only recourse is to spend more time waiting to talk to other people until you manage to find one who can help you.