I understand most of the debate regarding the choice has largely died down, but I just wanted to voice my opinion with regard to the choices.
So this turn we got confirmation that Rulwyna was in fact a heroic character, and that our choice to have Rulhuthyn raise her likely gave her the push into heroic martial versus some other trait. The war against the Hathatyn is going reasonably well, with our technology advantage (iron) and heroic leader mitigating what is likely more advanced tactics and their own heroic leader as well.
The main question now it seems is what Rulwyna should do. AN has given us four choices, and I would argue the four choices, while all viable, are not equal.
I'll begin with what is probably the worst of them:
[] Run away to the north
So, this essentially has Rulwyna impose a self-exile on herself, heading to the nomads who are apparently "peaceful" (for now). This choice "fights" against the establishment of hereditary rule, but I think everyone can see the huge downfalls with this choice. If this choice had been instead to go to the Stallion Tribes or some periphery state, this might have been an interesting as none of the technology / skill would leak out, but as it stands it just seems like we're gifting the nomads primitive horseback riding and a heroic martial leader. While it has been stated that the horses are only able to act as couriers (and the occasional elite horse archer), the selective pressures imposed by the nomads will likely raise large enough horses for horseback archery much faster than us, if only by necessity.
[] Begin diplomacy with the Highlanders
This is the second diplomacy option, and an option that seems a lot better than the nomads, but still is quite poor (in my opinion). While it is true that Lolwyna likely did not gain as much significance because of her poor diplomacy skills, this option will likely only have a limited chance to increase the diplomacy of Rulwyna. The narrative strongly hint at the "diplomatic" mission being just marrying Rulwyna to the prince in the hopes of consolidating the two kingdoms, and with HK's heavily patriarchal government system I don't think they'll take to Rulwyna being any more than a queen-consort. Sure, we might get a few offsprings that would be able to claim the throne to the HK in a generation's time, but this also then reinforces hereditary (versus meritocratic) rule for us. Furthermore, that's not even accounting for if we fail the diplomacy roll and causing a possible diplomatic incident that we don't necessarily need.
As for the voters who believe that this option will be the first steps to establishing vassalage over the HK, I again ask if you are willing to switch to a hereditary system to do so. Diploannexing another country requires integration and at least observance of their customs (at first). Personal unions indicate that the ruler is not simply the king of an enlarged state, but rather he/she is the king of each respective country. As such, they must observe the customs of each country, and can't simply go in and start changing all of the rules of the PU'ed country. If you want to successfully diploannex the HK, you'd need to establish something that can shift their social values even more closely to ours without affecting our social values overmuch (yes, the codification of laws was good, but in the end they codified their own laws, not ours): organised religion would definitely be a driving force, and given the proximity if we build up our religious authority / pilgrimage the HK would likely be the first to feel its effects. So while I support the concept of eventual expansion, I don't think simply sending off our Martial/Mystical(?) hero off on a diplomacy mission will lead down this path (or at least down the path to our favour).
[] Forge a new path of war
As you are likely seeing from how I'm writing this, I support the science option. However, I would not be against the martial option either. While yes, it is redundant in that we are winning against the Hathatyn already, war is war and one can never be too sure. While I am not sure why people think that choosing this will alleviate the martial excess (if anything, this will lead to new innovations that might bump our martial scores even higher. We have main/secondary war missions to send out people to fight), I also concur that as long as we can keep stability up the martial excess will remain a problem and not a disaster (the mega-project "The Games" I think will help with this, providing a way to integrate martial training and ideals into a more social aspect). Furthermore, as AN mentioned we are "schizophrenic" in our technology, and I think that is especially true in martial technology. We have been (I hope) leading in material advances, first with recurve bows, then chariots, and then iron, but I think our military tactics are lacking. Sure, we have massed formation, but we need to have martial discipline and a coherent command/logistics network if we want to properly leverage these advantages. Right now, this war is the perfect chance for us to look past anti-raiding tactics and focus on strategic development against an (supposedly) easy enemy.
And if I'm allowed to be blindly optimistic, I'm honestly just waiting for proper pike formations. Chances are not in this war, but...
[X] Attempt to finish her mother's work
Yeah, I'm choosing science. I understand some people are concerned about how jumpstarting technology can actually hurt in the long run, as you don't research all the things in the middle, but I frankly don't think this is actual gunpowder. Note that it said Lolwyna was "burned" and that it may have had something to do with fire and water. Naptha is a likely guess, or just some kind of flammable liquid. I suppose we shall see but as PowerofMind stated this can be a huge boon to our religious authority. By showing that we have the power to create "unnatural" phenomena, we can effectively "one-up" any local religion (unless they have something similar, in which case we'll at least have a drawing point). If nothing else this is yet another step forwards in alchemy (ever so slowly approaching chemistry, although that is still millennia off).
For people who don't think it's a good idea to send a martial hero off to do research, it is stated that Rulwyna seemed to have the raw knowledge to carry on, although she is lacking in experience with the research. So while it isn't likely that she'll make an immediate breakthrough (barring lucky rolls), so long as she doesn't catastrophically fail we'll likely at least know what Lolwyna was working with. If anything this will reinforce the meritocracy and further drive the distinction between heredity and meritocracy: yes, Rulwyna is the descendant of the previous king, but she has risen up to her currently position of her merit. Instead of currying favour with the nobles in other nations, she is utilising her skills to bring benefit to the Ymmri.
Oh, and the whole gender debacle. This choice (and the war choice) will likely delay the encroachment of the patriarchy for another handful of turns and may even secure a permanent spot for women in warfare/logistics. I personally don't get why everyone is so fundamentally against the patriarchy, especially in a Bronze/Iron-age society. Infant death rates are still atrocious and forced marriage (whether by force itself or by coercion) is commonplace. Women have to give birth to maintain population rates, and we have seen this throughout our civilisation's history (even in the earlier turns, when we were supposedly less patriarchal, even the king had three to four kids of which two died). So long as we can recognise exceptional talent regardless of sex (Lolwyna and Rulwyna is a good example) and maybe even get a legacy that acknowledges this, I'll be happy.