Well, in your shoes, I'd be inclined to use two PICs and just step through the ADC channels to pick out out a 'non AC' signal (ie a dead element), else you're looking at a fair bit of 'gumph' just to put in between your 16 'monitored' signals & the PIC. (ok, so I know your boss said no multiplexing....but would he know that the ADC pins are multiplexed internally anyway?!!)

Also you make no mention of how quick you need to be alerted....is there a 'failed heater response unit' on hot standby looking at the leds, is a minute or two ok, must this be notified within a second etc.....such requirements all help steer the final deployed solution.