AMZ Mover
342 Harbor Wy, South San Francisco(650) 770-6633
Open SaturdayWebsite
6 moving companies in South San Francisco list long distance moving in their own details, 3 of them with their own website. All of them are below, with address and phone number.

Order: moving companies with a working website first, then by how complete their details are. Nobody pays for a spot in this list.
6 of the 14 moving companies in South San Francisco list long distance moving in their own details (43%). Not every company fills in everything, so the real number may be higher.
Nearby: San Francisco (33, 8.3 miles), Oakland (6, 13 miles), Hayward (3, 18 miles).
This is what the companies list themselves. If in doubt, just ask them.