Jake,
I like your thinking. Unfortunately I don't do a lot of river fishing these days, let alone swinging, so not much help on specifics there.
That said, I kinda get where you're going with this. And having dabbled a bit with custom lines, I'd suggest getting some hollow core braid and simply stuffing it with whatever recipe of T-lines you want. This would circumvent the welding issue completely since you'd only have to secure the rod end of each section with an external nail knot using lightweight braid, Kevlar thread, or similar thin/strong material. Maybe with a touch of adhesive to smooth it out. Same connection with the running line. This is possible because the hollow core tightens under tension creating a "Chinese finger cuff" which grips with increasing strength.
Or, just stuff with a thinner line of choice to create a custom running line that gives you the desired stiffness and handling qualities, but maybe with a thinner diameter to reduce water resistance (fish deeper, swing across current slower, etc..).
If you try this, the stuff you want is
Jerry Brown Hollow Core Spectra . Not cheap but they do sell it in 150 yard spools. Not sure what weight line would be best for river fishing, but thinking the 60# or 80# would be about right.
Super interested to follow this, and thumbs up for thinking outside the box!