For the liftout section, assuming it lifts straight up, take a look at the lift bridges on the Northeast Corridor. No need to build a working model of their mechanism, but just look at the complicated anchor frames. Then build something similar at both ends of your liftout, with matching frames on the fixed and moveable sections. The "wires" would be brass rods, or maybe pieces of upside-down code 40 rail, with the two pieces at each joint overlapping. Make sure the overlap is on the fixed layout, and that the fixed section doesn't extend over the liftout. Bend the very tips of the overlaps up slightly, so the pans don't snag, and you have a simple, reliable, and easily removed liftout catenary section. No need to physically connect the two pieces, as the pans will slide over the two overlapped sections.
Why rail? The flat base would be easier to solder, and make a more durable joint, and it might be a little less likely to deflect vertically. The actual catenary wire could terminate at the frames, making sure that it's even with the bottom of the overlap sections. One way to do that would be to extend the overlaps on both sides, and bend them upward slightly on the "catenary side", so that the pans would follow them down from the wire level, rather than trying to make the wire and overlaps exactly match.
I did much the same thing on my MILW staging track. It doesn't move, but the wire terminates just inside the tunnel portal, and the rest of the track uses code 40 rail for the overhead. The end of the rail is bent up, so it's higher than the wire, and the wire is angled up from the first support frame, so it terminates above the rail.
