The current module weight is absurdedly high.

The weight of the module in the systems table is 9999. Yes the module must run later than things like jQuery Update. However there are things that have to run after JSA (Parallel module for one). Having extremely high (or low) module weights just encourages a race to infinity and makes it difficult to actually see what should be heavier (or lighter) than something else. The better way forward would be to make the weight +10 whatever it needs to run after. That still gives something else opportunity to go in between. In this case I believe that the only thing that JSA must run after is jQ Update. So a weight of 109 for JQA would suffice.