SSA Track 1: Unchained TR150 Rune
Why is this in your plan after everything you said about needing to spend our time on actual Akatsuki counters? At least the Icarus Rune has potential value on the battlefield, especially if deployed by surprise.
If you mean for it to increase our total research time, I'm not super sure but let's figure that out. At our current TR125 state, we spend 21 hours per subjective day dilated, taking 16.8 solar hours in total. Add in 3 undilated hours of FOOM and we spend (rounded) 20 solar hours per subjective day. This equals a free subjective day every 5 calendar days. If we gain access to TR150, we spend 21 hours per subjective day dilated, taking 14 hours per day, plus 3 undilated hours for a total of 17 solar hours per subjective day. This means we can complete 7 subjective days in 119 solar hours, within a rounding error of 5 calendar days. In other words, a second free subjective day every 5 calendar days.
This means that getting TR150 only saves us one subjective day every 5 calendar days, in relation to the TR125 that we already have. A rune cycle is 5 days, right? Let's say we spend four cycles on this rune, since it's "Hazou thinks he could maybe do this rune". Call that half of our prime real estate for 20 days, or for convenience a flat 10 day investment. This rune takes 50 calendar days to break even (and it doesn't kick in for 20 days, so it only breaks even 70 days out from now).
That's nontrivial enough that I think we have to seriously ask how long of a time horizon we're still planning for. The comments I heard from Naruto seem to suggest he's inclined to wait until Akatsuki proper gathers at the rift site, at which point we somehow approach and assault them, sealing the rift behind anyone left inside and then yoinking it to an undisclosed location. This means the confrontation happens more or less on Akatsuki's timescale, which... we don't have a very good way to estimate. We could play dangerously by letting them sit at the rift for a while before striking, but we run the risk of them finding Pain unexpectedly early.
Do we think we still have 70 days left? This research is a net benefit if we do and is a net penalty if we don't. If we aggregate across our entire probability estimation, is the increased odds of victory across the probability chunk where we do have 70+ days left stronger than the decreased odds of victory across the probability chunk where we don't? What even
is our overall chance of victory here? Do we need to make gambles like this or risk having no chance at all? Do we think we have it in the bag and shouldn't risk increasing any extant chances of failure?
(Also modulate all this by an appropriate amount if you figure the research will take more/less than 4 research cycles. If you think it's 3 cycles we only need like 53 days left, if you think it's 5 cycles we need a full 88 days.)
All in all, I'm genuinely unsure of where I stand here. I won't ask you to remove this from the plan, but I think we do need to have a more complete conversation about this and get our priors in order before we commit to gambles that only pay off under certain priors.