log_min_duration_statement setting is ignored
You were close. Your last idea is actually the way to go:

log_statement = none
log_min_duration_statement = 10000


Then no statement will be logged, except those running longer than 10 seconds - including the query string itself. Logging may have seemed to stop because 10 seconds is a high threshold. I am using 2 seconds normally, but YMMV.

This related answer on SO has more:
Cannot get log_min_duration_statement to work