I'm still working on how I want to set it up so that the river can still flow, yet can also be stopped. Any ideas for that would be welcome.
I'd say you need to make a semi-permanent dam the river above the gate, then at the gate itself build and lever-link a wall of floodgates as well as wall of vertical bars/grates. Then you will be able to start and stop the flow of the river at will, as well as permit and forbid passage of aquatic creatures while the river still flows. Once the bars and floodgates are linked properly and functional, you can deconstruct the dam.
As for making the dam, you'll need to temporarily divert the water so your dwarves can work. Most of these ways involve digging channels and other permanent landscape alterations which you may wish to avoid, so if I were you I would place a series of pumps spanning the river and an above-ground constructed aqueduct to divert the water. You could try sending it back into the river below where you want your dam, but it may flow back upstream, I'm not sure. The only other option I can think of would be to create a giant cistern, but that comes with it's own problems. Firstly, if you underestimate the amount of water and run out of space in the cistern, either the cistern will overflow, or the pumps will stop functioning and your masons will drown building the dam. Secondly, you'l need to drain the cistern back into the river below the dam once it is completed, so you'd have to build a drainage duct and floodgate controls. Thirdly, the cistern may have to be multi-z-level. I don't think the pressure would cause any problems with the drainage (unless a tree grows in the way), but it means you'd need nine pumps (one for each tile-width of the river) for every z-level you need to raise. And a nine-pump-wide pump stack is no small undertaking.
If you pulled it off though, it would be an amazing feat of dwarven engineering. If you use the cistern method I described, I'm going to demand incremental screenshots of its construction and operation. Also, don't forget to make incremental saves and back-ups, it would be very bad if you lost the world to a hard drive failure or something.
How are you going to make the walls line up and be contiguous across region tiles? Unless there's been a change I'm unaware of, you can't set half of your embark in one region tile and half in the adjacent tile.
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Oh wow, I spent a long time on this. I was bored. :/