How to capture byteman logging if System.out logging is disabled?

Issue

• We need to use byteman to troubleshoot issues at runtime. For this, we have developed some byteman rules, which use System.out.println("...") calls to log the desired information. This works fine in our development environment.
  In our production environment, however, the logging of System.out is disabled, as per the instructions from ¹.

• How can we change our byteman rules to log to a file, or use a logging framework?