I think your choice of discount rate is going to fundamentally alter your investment decision, it's not just some kind of marginal technical tweak.
In practice either you discount fairly heavily, as most public projects do, and end up putting most of your money into solving short-term suffering (as I think you should), or you discount lightly, and put most of your money into possible future catastrophic risk mitigation.
I don't see how this is "computational convenience" - it's fundamental.
What do you mean by "using discount rates on a case-by-case basis as a convenience for calculation"?
I don't find your dissertation discussion very convincing (but then I'm an economist). I worry a lot more about the existing real children with glass in their feet right now (or intestinal worms or malaria or malnutrition or whatever) than the hypothetical potential children of the future who don't exist yet, and in any case when they do will live in a substantially wealthier society in which everyone has access to good quality footwear.
Let me explain my position - first, I agree with rejecting a pure time preference, and instead doing discounting based primarily on expected growth in incomes.
For me, the expectation that in 50 years the average person could easily be twice as wealthy, leads to quite heavy discounting of investment to improve their welfare vs spending to alleviate suffering from extreme poverty right now.
It's possible I haven't thought this through thoroughly, and am explaining away my lack of enthusiasm for your choice of 5 causes to the neglect of the classic Givewell/GWWC choices. Perhaps there is something to do with efficacy there - that I'm unsure of the likely impact of funding immigration advocacy, forecasting, and more research.