Been shaving my head for 20 years and have never had a good head-shave with a DE . . . and I've tried, lots. From the mild Blue Tip Super Speed to the Sledgehammer Slant and with all blades from Merkur to Feather. I've also shaved my head with a Shavette, a Feather Artist Club and a Wapienica straight razor with the same kind of result.
The very best razor for shving the head is the Mach3. I have never had a problem with a Mach3 clogging as the blades are well spaced and open at the back.
Forget the brush and expensive soap too. The hair on the head is finer than on the face so doesn't need softening like the beard so just wet the head, whack on any old brightly-coloured gel and whip it all off again along with the hair.