^^do you have pictures of the springs you can post?
^are the cross wires the wires that are intertwined in the burlap? If so, I have been hearing that using vinyl will do the same thing and better protection then burlap.
There once was a larger wire wrapped in brown paper to prevent noise. It was attached to each spring with a sheet metal band. Those were eventually deleted.
The burlap with many smaller wires purpose is to prevent the batting or foam from going through the springs. They hog ring that to the springs and it serves the same purpose as the larger wires, for a time anyway.
Upholstery shops sometimes replace that with some other material. I've seen home flooring type carpet used there but it's placed upside down.
If the springs are tied together left to right, you'll have a softer seat that wont hold up as long.