Yes, this would be a pay for success contract. And a "prize" or outcome payment of $1b would not be necessary. By using a generic drug, you can enter into phase 3 trials immediately, and it can cost less than $10-15m to obtain regulatory approval (100x cheaper than developing a new patented drug over 10-15 years) - see https://dndi.org/wp-content/uploads/2019/10/DNDi_ModelPaper_.... See Figure 1 on page 17: Out-of-pocket costs per stage of development for eight projects in DNDi’s portfolio.
You likely don’t need a standard phase three trial. If you are within the phase 1 safety dosages (that’s the data you’re using under 505(b)(2) anyway) you can just do a smaller study. Power it as high as you want/need. Typically any physician can do such a study. Doctors can read your paper on the study and decide whether to use the therapy you studied.
Yes, it may be possible to update standard of care with a robust Phase 2 RCT that convinces doctors, especially for a pilot. Phase 3 trials for a repurposed generic would be more expensive, but a new label indication would provide further incentives to update SoC because doctors and pharmacies would be less exposed to liability for prescribing off-label.