Yes, I've fixed it above. It should have said viewport width.
I kept thinking about rivers, and eventually ended up with a map/color indication scheme that I thought might work. After that it was mainly a matter of work (although I did get a reality check regarding feature shell features: they're unloaded when the shell goes out of focus [or something like that], rather than remaining loaded once loaded initially, as I thought I'd seen earlier, and may have claimed on the forum).
As with regions, rivers are given random unique names (rivers are called "The River of Y"). My attempts to find some mapped/exposed logic for selection of feature names hasn't been successful (although Quietust provided a mapping of words to some categories, allows for some variation in the "X" part of region names). MaxTM provided a script that almost worked in fortress mode for renaming things using the method you mentioned as its core. However, it doesn't seem to be trivial to replace the vocabulary since I don't have suitable ones, so I won't bother with renaming for the time being.
Just don't try to reroute every river on the map: my 33*129 test target world has over 1000 rivers and most world tiles have a river in them. To make it worse, there is no way to save "work in progress", so everything will have to be done in a single session (you can exit the script and reenter it, but DF itself will have to be in the same state). The exception to that is if you're working during pre embark (as opposed to during world gen), in which case you can do "save embarks", save, abandon/retire, and then continue.
Edit:
Updated to 0.22, 2017-11-18.
Added missing character causing selection of another river while one is selected to erroneously flag the sink as being in error.
It can also be noted that DF doesn't seem to like new rivers: I created one in pre embark mode, but it failed to show up on the region map, despite the known required structures looking correct. Rerouted pre existing rivers have displayed correctly when tested both during world gen and pre embark.
Edit 2: Creating a new river, embarking elsewhere, abandoning, and then re-entering pre embark shows the new river on the region map, so it seems to be a matter of DF not reacting to this hacking until the data is read anew. However, that still means you can't add a new river for your imminent embark, and that your large scale river creation projects won't show up in DF until the game is saved and reloaded (and I assume the same issue exists for creating new rivers during world gen).