What if the channel was vertical an placed at the center of the pyramid?

     /| |\
    / | | \
   /  | |  \
  /===/ \   \

blocks surface at the center of the floor while it's being built.

The entering tunnel is gently sloped but doesn't have to reach the top of the pyramid.

I guess it would be easier to build since the the walls of the channels are kept in place by the weight of the whole structure.

I don't know about the bladders though.