The small wires can be replaced in the burlap, but you will need to cut off the paper-wrapped larger wire and re-thread it into the new burlap, then re-twist the small wire around the larger paper wrapped wire.
These small wires were used to provide a connection between the zig-zag (No-Sag) springs, so when one spring was depressed (as in; pushed down, not in the sense of 'made sad'
get it?) it would bring the other springs with it.
Using a few layers of Burlap will work as well. Just make sure you hog-ring the burlap to the springs.