The ceiling joists are 2x6 or larger. The flexure from walking in the attic is probably exaggerated, and is really only noticeable in the large L-shaped area. Unfortunately, it is right near the attic stairwell.
The house was built in 1921 and the people who bought it rennovated it themselves. Walls were changed, but I think they cut corners and did not apply additional coats over the tape.
Here's where I'm not clear on the paper tape. I know you are supposed to put a thin layer of joint compound over the mating edges, then apply the paper tape. How much pressure do you apply to the tape to get air bubbles out? Do you apply the coat over the tape while the layer under the paper tape is still wet? The do-it-yourself store near me said not to use the mesh tape on ceilings, I should only use the paper tape. What do you think?