First Circle of Healers (1)
Orc Cordial: Orcs have medicine of a sort, a cordial whose taste is horrendous but who gives strength to the body anew. Amazingly enough, just like the excuse for alcohol they brew, Orcs have very little idea on how the cordial work. It doesn't seem to be on applications of the Discord, considering the drink work without draining the life from something else. Studying it could be useful, notably because it could open the way to other less noxious mixtures. Ideally less foul ones to taste too.
The Circle of Learned (2)
Ring of Durin (Special): You've learned by Galadriel of the existence of the Rings of Power and the terrible strength they possess. One of these infernal contraption is in your reach, to the finger of Thrain in truth. You learned that Dwarves seem to be more resistant to the corruption than the other races but you are still eager to learn of the secrets of this artifact. In your experience, nothing created by Sauron is without danger or aftereffects and these rings seem to be no exception. You would also learn about their workings to better destroy the One if it came into your reach. [Try to study Durin's Ring]
Secret of the Dwarves: Dwarves can reach in the Music and their parts are very near the parts you sung at the beginning. Earth, Fire and Craft are elements you know and would like to practice again. Fortunately, there are some runes and items of power scattered in the depths of Moria. With these items, not only shall you be able to reconnect with these parts of the Music but perhaps could you teach to the Orcs to be more like the Dwarves than ever, absorbing many of the qualities associated with the Children of Aulé. After all despite their wars, the two races share many traits already. [Study Dwarf Magic]
The Feandur (Servants of the Soul) (2)
Doomsman's of the Valar: Of Mandos it is said he gathers all willing spirits to his halls and there they find respite before being sent to their destination. For the elves whose fëa doesn't leave the world, there is judgement and purification, for the Men who leave the Circles of the World there are vessels to bear them across the void to the fate the Valar know not. Of the Orcs nothing is said and many are doomed to uncertainty when they don't know. To urge your charges to look to Nämo is to urge them to consider the afterlife and their place in it. And perhaps at last adopt proper burial rites.
Visions of Lotus: Your Orcs discovered plants whose smoke give visions. Such visions calm their restless hearts. Used in the worship of Irmo they could be the focal point of the ceremonies. You wonder what a holiday dedicated to dream can look like. These herbs can help in that. Warnings about decadence aside, the Orcs still have instincts to violence who need to be leashed and dreams and lotus are a good way to do so. Who knows with any luck some remember untainted fragments of their former herb-lore to make potions more directly useful.
The Other Valar (1)
The Warriors of Heaven: Orome and Tulkas are the warriors of Arda and Nessa the wife of Tulkas is no less fierce than them Orome is the mighty hunter who teach both the respect of the prey and the art of the chase, while Tulkas is the warrior that defend the weak and laugh while in battle. If you want to make your flock warrior for the light, these three are perhaps the most appropriate to teach them about. Unfortunately teaching both violence and the need to restraint is very difficult and could perhaps backfire. Yet war is a part of Arda Marred and none should ignore those who weave it in the Music.
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I'm going with the cordial because it might just be the only thing in existing orc society that is worth keeping. If we ever go for intrigue options like the infiltration thing, it might help our orcs ingratiate themselves with the other clans if they make better cordials and better booze. Also, it will probably do a lot to alleviate their racial shame and self-loathing to know that there were things they got RIGHT.
Durin's ring is obvious, but I choose the dwarf stuff because our orcs have already been apprenticing themselves to dwarves and it would be a shame not to build over a foundation if it's already there.
Mandos I want because fear of death and eternal damnation is basically the biggest reason radical extremists become the nutjobs they are in real life. This has been the case throughout history and if we can cut this off at the source so early on (or so late), we should.
The Vision of Lotus seems like it would help render "independent" orcs actually susceptible to subversion, since I don't see them actually believing our infiltrators on anything in their current state. Recall that they are in constant physical pain, as seen of Palantir pre-healing. If the Lotus Flower helps dampen that, I'm all for it. Especially if it provides them with a form of relief during months and years of (re-)becoming the monster.
Personally I think that sort of infiltration is better not tried in favor of us trying carrot and stick diplomacy personally instead, but then again they ARE different categories entirely so who knows what votes will happen?
As for the last option, I chose the warrior Valar because I damn sure do want my people to be good warriors, especially when the rest of the focus has been on healing and making love instead of war.
As Ronald Reagan said when hippies protested him with signs saying "make love not war," "I don't think they can do either."