Another brute force approach: The are nine conditions to check for the logic input not being true -- all 0's on the input or only one input being 1. This can be done with nine 8-input NOR gates.
For the 8-input NOR gates connect each gate to the 8 logic inputs as follows.
1st gate-- All logic inputs connected directly to the respective gate inputs (all 0 check)
2nd gate --Logic inverter connected to first input, all other inputs connected directly
3rd gate -- Logic inverter connected to second input, all other inputs connected directly
4th gate -- Etc.
The outputs of these nine NOR gates go to a 9-input NOR gate (the Output).
The nine 8-input NOR gates thus determine if all inputs are 0, or if any single input is 1. Those are the conditions for an output 0 (2 or more logic inputs high criteria not met).
Thus if any of the eight gate outputs are 1 then the output NOR gate is 0.
If all of the eight gate outputs are 0 then the 2 or more high criteria is met and the output NOR gate output is 1.
I believe that will work.