that would mean that as the average node "quality" goes up, we become even more tolerant of even worse nodes.
That only holds true if the actual mean quality increases. If $NORM goes up (or down) purely as a function of how many votes are cast in total (which it will), then using -$NORM seems perfectly rational.
Instead, how about maybe something like -20 + $NORM.
That also suffers form the same problem as just using -7: it puts an arbitrary fixed point into things which becomes problematic if $NORM changes greatly from where it is today.