Need help with PML for 2D Acoustic 2nd Order Wave Equation in Matlab

I've been working on a 2D Acoustic 2nd Order Wave Equation in Matlab and but doesn't seem to want to work quite right. If I set the damping layer as a constant the simulation runs but with a lot of reflection. If I take the quadratic approach to "ease" the wave into the damping layer, the simulation grows an instability near the outer edge of the damping profile. I've seen some first order electromagnetic PMLs on this forum and I was hoping someone with PML experience might be able to find where I'm going wrong. I'm including the derivation and the Matlab code.

this would be very interesting for me also, any luck yet?