Sorry, this is going to be a “you’re doing it wrong” comment. I will try to criticize constructively!
There are too many arbitrary assumptions. Your chosen numbers, your categorization scheme, your assumption about whether giving now or giving later is better in each scenario, your assumption that there can’t be some split between giving now and later, your failure to incorporate any interest rate into the calculations, your assumption that the now/later decision can’t influence the scenarios’ probabilities. Any of these could have decisive influence over your conclusion.
But there’s also a problem with your calculation. Your conclusion is based on the fact that you expect higher utility to result from scenarios in which you believe giving now will be better. That’s not actually an argument for deciding to give now, as it doesn’t assess whether the world will be happier as a result of the giving decision. You would need to estimate the relative impact of giving now vs. giving later under each of those scenarios, and then weight the relative impacts by the probabilities of the scenarios.
Don’t stop trying to quantify things. But remember the pitfalls. In particular, simplicity is paramount. You want to have as few “weak links” in your model as possible; i.e. moving parts that are not supported by evidence and that have significant influence on your conclusion. If it’s just one or two numbers or assumptions that are arbitrary, then the model can help you understand the implications of your uncertainty about them, and you might also be able to draw some kind of conclusion after appropriate sensitivity testing. However, if it’s 10 or 20, then you’re probably going to be led astray by spurious results.
I agree that EAs should pay more attention to systemic risk. Aside from exerting indirect influence on many concrete problems, it is also one of the few methods available to combat the threat of unknown risks (or equivalently increase our ability to capitalize on unknown opportunities). Achieving positive systemic change may also be more sustainable than relying on philanthropy.
In particular, I like the global governance example as a cause. This can be seen as improving the collective intelligence of humanity, and increasing the level of societal welfare we are able to achieve. Certain global public goods are simply not addressed, even despite much fanfare in the case of carbon emission abatement. Better global governance would thus create new possibilities for our species.
A full-fledged world government might be the endgame, but in the meantime small advances might be made to existing institutions like the UN and the EU, as you suggest. Unfortunately this can be very difficult; removing veto power in the UN Security Council is a case in point. Fundamentally, any advance on this front requires countries to sacrifice part of their own sovereignty, which seldom feels comfortable. But fortunately the general trend since WWII has been towards more global coordination, the recent visible setback of Brexit notwithstanding. My personal belief is that any acceleration of this trend could have huge positive consequences.