I've found it's the lower seatpost clamp that does most of the work on my Swift. It can hold the post in place all by itself, which the upper one cannot do. The post should be free of lubricants, as you've discovered. I swapped the original seatpost with a (now, older-generation) Cane Creek Thudbuster with an extra-long post of the same diameter as the original, which is ~34mm. The Thudbuster adds weight but makes the Swift quite a decent bike for bumpy hard-pack dirt roads and gravel paths.