With enough Antimagic fields, you could bypass the puzzle entirely bu deactivating both the instant teleportation, the *blowing out braziers* effect, and the magical sense location effect, thus enabling you to manually go through all the rooms with no hassle and light all the braziers.

Even Better
Since your antimagic field deactivates the no planar transportation thing, you could open portals above the antimaic field to the elemental plane of fire, let dozens of fire elementals onto the material world, and let THEM do the lighting for you.