This is my preliminary build.
Commoner 20.
Stats.
STR 12
DEX 12
CON 12
INT 18
WIS 13(or CHA 18, I'm not sure if Commoners get the extra stat points from leveling up)
CHA 11
Skills Blacksmithing 23, Chemistry 10, weaponcrafting 23, armorcrafting 23, Medicine making 23, Healer 10, Teaching 23, Masonry 6, farming 3
I'm starting in Saath, it's the only city that didn't fall, and I can always send help to the other cities to turn the tide.
I'm going to start out, by earning a fortune selling masterwork items, then I'm going to buy some slaves, set them free, and offer them the chance to become my apprentices, then I'm going to teach the ones that accept, while continuing to accumulate wealth, this is what I spend the first decade doing, at this point I should be rich, as my own work is seen as the best you can get anywhere, and my apprentices work are also top quality, and go for significant prices.
Now I'm going to spend my money buying land, 10 years has passed, so half of my levels have been retrained into monk, I put the resulting 20 skill points in farming, and use a combination of my farming and blacksmithing knowledge, to make farming tools that are much better than what's currently available, and I'm not just talking better plows and such, with a bit of modern knowledge, and 23 skill ranks in both Blacksmithing and farming, inventing the seed drill, a muscle driven harvesting machine, and other such things should be well within my capabilities, my chemistry skill let me develop cheap and easy to produce high class fertilizers, and my farming skills help me with calculating the ideal crop rotation, so my lands should produce many times normal amounts of food.
I spend 10 years more on doing this, letting me retrain my final 10 levels to monk, giving me yet 20 more skill points, I use 13 of them to bring my healing skill up to 23, so I can be the worlds best doctor as well, and the other 7 to bring my Masonry skill up to 13, so I can also teach super-high quality stoneworkers.
Now being rich and having my own domain, I begin to do weapon development, I don't expect to mass produce these weapons, but I should have about 10 years before the Dothraki invasion begin, and even longer before it attacks my lands, so I should be able to amass a pretty good store.
I don't really want to introduce guns before I'm more established, so I make Hwacha's, mass arrow launchers will be a great weapon against the Dothraki, and they wont be as game changing for other warfare, as big shields should be remarkably effective against them.
ideally I get warning in time, and I manage to send Hwacha's to Sathar, breaking the Dothraki invasion before it can begin, but if I don't get warning in time, I wait until I get some form of call to arms, or until the siege of Mardosh begins, that siege last for nearly 6 years, so it should be easy to send aid then.
I don't really have plans for afterwards, except to keep amassing wealth and power, and work to abolish slavery in Sarnor.
Of course these are very lose plans, the me who was inserted would refine them countless times, but I think it's a doable way to save Sarnor.
And yes I took absolutely no combat skills, I don't expect to get into battle initially, and as I gain Monk levels, you need ever greater foes to threaten me, even with my lack of skill, and I will be finding an unarmed combat instructor, so I can learn the skills that will help me in a fight the slow way, if I remember right, you can get up to 5 ranks in a skill though training in this quest, that amount of skill rank plus being a level 20 unchained monk, should be enough to defeat most anything short of an army prior to magics return, and by the time magic return, I expect to be in charge of a powerful nation, so I wont be expected to do the fighting solo.
Edit. Also I begin to retrain into Wizard once canon start.
Maybe
@DragonParadox would have a better idea on this than me, but I find it hard to believe you could do this with just class skills. You would have to take some social skills with finagling with feats or some such simply to ensure you had the influence necessary to implement the changes you wanted, and even with maxed out teaching profession skills, you could only prepare so many Level 5 experts, their capabilities would be limited in years of waning magic anyway, and you would waste most of the time both trying to keep your position secure and trying to build up assets to build the assets (or the tools to build the tools in this case).
If you had a century to prepare, you could probably build up the powerbase necessary to change things within a century, but your best bet to do that is to actually schmooze and get other people to do the work for you, not try to be An American in the King Alexi's Court as they case may be, and trying to "teach the savages" with barely three-four decades to work with and having to spend most of that time preventing the very reason Sarnor fell--internal squabbling and treachery--from swallowing you up and your work with it.
My plan is really more to become very rich, and make a few hundred guns, it's not like I'm forgetting my previous life, so with Blacksmithing 23 and Chemistry 23, I can make guns easily, then I just need to train my apprentices to make the bullets, and the Dothraki get a close encounter with guns and cannons.
But I should probably go for another city instead of Kasath, Mardosh seem a good idea, it held for nearly 6 years before falling in canon, with the vastly improved gear I could supply, I can very likely prevent it's fall.
While I disagree with the idea that a mundane crafter could help much. Industrial revolution takes ages, after all.
Full industrial revolution takes ages, training a couple dozen crafters to make Hwacha's don't, and with years to hoard arrows for them, I can certainly shift the balance of the war, it's not like the Sarnori were that badly outmatched by the Dothraki, they lost but it took a long time, with better gear and some super weapons, the outcome will be entirely different.