I do not believe there is such a thing as overkill, except where your checkbook is concerned.
However I am not sure whether your proposed arrangement is the wisest use of money.
Hog panels usually have pretty big spaces, don't they? Anything inclined to go through, and able to get up over your band of sheet metal along the bottom, is going to easily be strong enough to rip apart your chickenwire IMHO. So I am not sure the chickenwire serves much purpose there.
Second, will this run have a top on it, or at least a very well-installed frequently-checked hotwire above the top of it? Because unless the answer is "yes", many many predators will just go up *over* the fence rather than bothering with your fencewire.
I would suggest putting a SECURE STRONG STRONGLY-SUPPORTED top on the run -- meaning nothing larger than 2x4" mesh, and nothing weaker than maybe 16 gauge wire for it -- if at all possible. If already have, or if you cannot (b/c of size/shape of run) but want to run an electric wire on the fence to mostly climb-proof it, then I would suggest using 1x1 or 2x4 wire instead of chickenwire, and probably skipping the hog panels altogether.
JMHO, good luck, have fun,
Pat