I'm not even sure that the guard will support us if a fight breaks out when he comes back to get us
I was worried at first, but am now fairly confident that the guard (or the Elite, at the very least) would support whatever Captain Martin decides. They made their stand not based on the precise intricacies of jurisprudence, but based on their loyalty to the Captain (and with 3% chance of yielding, at that).
(It helps also that the guard now thoroughly disapprove of the attitude that has been revealed--and would disapprove even more with the words we've plausibly overheard. It should be a relatively easy sell to their subordinates... assuming there is hope of victory.)
So, our getting the Captain's support would probably allow us to recruit the guard. Reading the rulebooks, on the other hand, is unlikely to get us anywhere, since it was shown they don't care about the rules.
So even assuming we use a full two seconds, you still only have two seconds worth of thought. I don't think Keen Mind is really hyper-accelerating our thoughts, meaning that we only have the best result we can get from two seconds of planning, which is obviously not great.
The original idea hinged upon Lilly learning very-fast writing; the meta-power then selects the best plan according to the Lillies' judgement, and actual-Lilly writes out said plan.
(The big unknown is, in this case, how much computation the meta-power at the end allows. In total, we certainly get more than the two seconds worth of thought, but how much more?)
In the absence of such accelerated writing, we're left with the notion of generating revealing insights. There are certain key turns of thought that, essentially, dictate the rest of the plan (or from which the rest of the plan is easily built); these would be the main result of such an endeavor.
You're right, however, in that sample space seems to synergize with hyper-accelerated thought. We should be looking for such a power next (maybe the speculated bullet time from the Brave Blood ethos?).
And his [Rapid Iterator] could possibly create lots of prototypes in a short time, we have an Ethos that if I'm reading this stuff right develops them to their logical conclusion.
Sadly, Yolun "only" has [Iteration to Perfection], which to be sure probably does synergize with the foundational ethos [Rapid Iterator]. (Dungeon for quick prototypes + Yolun for optimization of prototypes) seems like a winning combo, especially with Yolun potentially integrated into the Dream (but regardless, with the collective communion).
Which is why we should grab [Rapid Iterator] next, if at all possible.