Groovy script can be used to plug in upon Jenkins initialization. Please make file with name init.groovy in your Jenkins home folder with changed logger names according to your needs. Here is a sample file content:
import java.util.logging.Level
import java.util.logging.Logger
Logger.getLogger("").setLevel(Level.OFF)
Logger.getLogger("org.apache.sshd").setLevel(Level.OFF)
Logger.getLogger("winstone").setLevel(Level.OFF)
I have tested this approach on Ubuntu and Windows and it kept permanently the log level changes. I believe it will work for other OS also.
More info in my article on this topic here.