We still have the problem of what to do when the reading is invalid on multiple sensors.
You've hit the nail on the head. IMO, the goal should not be to "eliminate" pitot ice. This may be all but unattainable. The goal has got to be a graceful degradation of the system if pitot ice happens. In my naive view, the former goal will lead to a more complex system, where as the latter to a simpler system. IOW, if we can't prevent pitot ice, force it to ice asymmetrically and force it to do it at the earliest opportune moment.
In the words of Sir Isaac Newton, If the apple doesn't fall, go shake the tree!