What I want, I think, is for the parser, having recognized one occurrence of job_statement, to at that point <commit> to it.

So, <commit> after each successfully parsed job_statement. Then offer an alternative that slurps up the rest of the file, as a dummy, to make the grammar match in the end.

I don't know Parse::RecDescent enough to express what I mean in code, so I'll try in Perl 6 rules, maybe that's sufficiently readable for you to translate it to your needs:

grammar Jobs {
   token TOP { ^ '$JOBS' <job_def> $ }
   role job_def {
       [
            <single_job_definiton> <commit>
            || .*   # if there is no way to parse
                    # a job definition, dummy-parse
                    # the rest of the string to prevent
                    # outright failure
       ]+
   }
}
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