I've used J-Clips but that was with different wire. With your combination of wires, I'd think using other wire would be best.
One thing I'll mention, based on bad experience. When you put the hardware cloth on, make sure it is connected well enough that a chicken cannot get between it and the regular fencing. Those birdbrains will push their way into openings you would not think possible. They may get in from the bottom, top, or ends. Sometimes it can be hard getting them back out. And if you are going to have baby chicks in there sometime in the future, consider that when determining how well to attach it.
I agree to never use plastic, either as fencing or the zip ties. The zip ties are better than they used to be, but any plastic will eventually get brittle.