Would it be possible to add functionality to Checkstyle (or even all of the
Static Code Analysis plugins: Findbugs, Compiler Warnings, etc.) that provides a
configuration option that will make the build unstable if either A) the number
of violations increased from the previous build or B) new violations were found
from the previous build.

These would be useful because the end goal of these plugins is to reduce the
number of violations; these options would discourage new violations and help the
overall trend go down, or at the very least not go up.