After asking a couple of buddies and some family into woodworking, I got absolutely no consensus whatsoever. So I went out and bought a 7 1/4 inch 60 tooth carbide tip blade at Lowe's for $15.
I double-checked with an employee there, and they thought it would have no trouble cutting through the wire. They were right.
Smooth as glass. Great cuts, no effort, and it allowed me to finish the job today fairly easily.