I think it's also supposed to increase the overall energy of the weather so bigger, nastier, more frequent storms.
It definitely would lead to more frequent, more severe storms since storms are largely the consequence of the transfer of energy poleward. The more energy that needs to be transferred, the more storms.

I think the equator is stuck being a convergent zone whatever you do, so it's going to be rainy,
Not necessarily. The equator is a convergence zone because it gets heated more than its surroundings, leading to low surface pressure, which leads to convergence. But, if you could contrive a situation where the equator gets heated less than the surrounding latitudes, then it would be a region of high surface pressure and divergence.