OK, so if we're aiming for precision, my projections leave out breaks AND HQs. I don't have any idea on what either rate is, so I can't include them. Given that both break/HQ rates will be the same across paths for the most part (I think,) that only affects the final cost number and shouldn't skew any of the general trends among what I've laid out. If break rates change based on variables like step#, tier of sphere, tier of chain, etc., then I imagine that it would point us even more towards the lower cost, lower-tier focused options, like what I said earlier. Don't think I said anything about these being complete cost quotes. ^^;; Estimates are estimates, and can definitely be refined further. Everything I'm doing so far is already stated to be disregarding sphere cost in the base projections, (since we're talking about farming them ourselves and not buying,) so since I'm already assuming that sphere cost is 0g in the beginning, cards won't really affect that portion of the projections even if they crap out a stack of spheres per success. The only cost for spheres anywhere in my math is for the associated crystals used to desynth them and chain them.
I'm not sure that up to 267mil in catalyst costs alone (baseline, no HQs/breaks included) can be called "negligible" even if you're gilcapped. :|