I too am playing GOTM 4, though it's been on hold since the beginning of July because when I have a free moment, I play a few moves of GOTM 6. My order of conquest was the same, and for posterity's sake, I left a single Sioux and Viking city when the dust settled.
Is more than one Sioux city building the Manhattan Project? If only one is, drop everything, spend whatever is necessary, and get a few spies over there. Bring two engineers and the best veteran defenders you can find. Put them ashore, and use the engineers to build a fort on the best defensible roaded terrain you can find. Move the pile around, find the Manhattan Project city, and spy on it each turn. As it nears completion, sabotage it. It may take two spies (sometimes 3, if they are not veteran) to get it, since non-vets are often captured when you target a specific improvement.
Since you now occupy the land across the channel (to the west of the core Sioux empire), incrementally rush build a transport there. Divert any nearby engineers and good defenders to it, too. Rush build, or just buy (210 gold), at least 2 spies, and get 2 or 3 more under construction for replacements in several turns.
Unless lots of Sioux and/or Viking cities are building the Manhattan Project, you can stop it forever, as long as you keep your spies on station!
It is riskier if you are not good at coordinating and controlling a large and complex plan, but there is another solution, too.
In phase one, you still need to delay the Manhattan Project a few years. Determine the number of Sioux cities you need to conquer. Build spies... triple the number of Sioux cities. I suggest at least 50. Get them into place on the Sioux mainland, along with some high-mobility units like mech inf, tanks, or even engineers.
Phase two... the execution phase (LOL!). Let them build the Manhattan Project. If you're already in Communism building vet spies, great. If you're in Democracy, declare a revolution and use your spies to nuke every Sioux city. Move your pre-positioned pieces into place (poised to enter all their undefended cities). Make absolutely sure you have all cities accounted for, then simple capture all the Sioux cities and exterminate the Sioux. All the Partisans will dissappear, too. Bring over all your engineers and clean up the pollution ASAP.
I once did this to a huge huge Celt empire, and had 305 squares of pollution to clean up. It took two turns after the nuking to control the pollution (the attack turn, plus 2 more). Fortuantely, my control number was about 27 due to the Solar Plants I had been able to construct, but your pollution target number will be 9 because it seems you are not to Environmentalism yet (since you don't even have SDIs built).
Hopefully, the Viking do not have Rocketry, or else they'll have nukes too. If the do, make peace, wipe out the Sioux, recover for a few turns, and release your now-veteran spies on the Vikings, LOL!
I know what city is building it, but I don't know exactly where the city is, and couldn't get to it in time if I did. 
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