Not so dense these days now we have the microcontroller. One to hand has 80pin flat, 28 pin soic, 32 pin dip, 2 off 20pin dips, 2 40pin headers plus descretes. 2 layer, 3"x 2".
I use a router by Bartell, a german company, It's at least 10 years old. Ive never failed to get 100% routing success. Vutrax, an americasn company, used to use it on their systems but they make their own now. Both systems are highly recomended.
I think a 2 input AND gate solves this problem. PWM to one input, on/off to the other, output to the panel. You can either use a gate per panel or use the AND function in your software.
The kw rating seems too high, also a cold element draws alot more than its rated current. Another possibility is your temp controller is cycling too fast.