After I had thought of this, I thought of offsetting rows of these bridges to make diagonal channels through the floor. This also worked well, because a pillar is about the same length as a horizontal brick.
I came to a problem when I realized that all the channels need to reach the chimney somehow. I somehow needed to make bridges between channels. Another reason I wanted to get rid of some pillars was that I don't have too many bricks left.
Initially, I thought, why don't I just use three bricks end to end, and span them between two pillars like in the other case? Looking back now, I'm not sure why I thought that would be a good idea. Joining end to end is probably the weakest way to span, and I am not using the shape of the brick to my advantage. I thought I could use the resin to prefabricate these beams but the resin is not magic.
I finally decided to use pillars of half-bricks in some places. The shape of the halves means that they can be wedged in place between two pillars and still provide some sort of support for the horizontal bricks.