You state:

Uranium atomic weight is about 238.03 moles per gram
Lead atomic weight is about 207.2 moles per gram
Difference in atomic weights per mole 30.83
When one gram of Uranium 238 decays into lead, about 31 moles of matter has been converted to energy.

Atomic weight is grams per mole, not the inverse as you put forward.

Uranium does decay into lead, after several intermediate steps, but it ends up as lead 206 and it takes 4.5 billion years.

In the decay process, alpha particles (2 neutrons and 2 protons) and beta particles (electrons) are given off. These particles have significant mass, especially the alphas, and account for most of the change in mass between uranium and lead. Not a lot is actually converted into energy, certainly far less than the 31 grams you conjecture, which means that the rest of your argument is fatally flawed.

I realize I'm wasting my time here, but hey it's late in the day...