When the peppermint parasol is used in combat for a free runaway, the message is "You hold up the parasol, and a sudden freak gust of wind sends you hurtling through the air to safety." Cut it down to "sudden freak gust" for SBIP safety. That should increment _navelRunaways. It should probably also increment a new parasolUses setting, which needs to be reset to 0 by "Man. That last gust was more than your parasol could handle. You throw away the shredded (but delicious-smelling) wreck that was once a useful tool." Cut down to "You throw away the shredded" for SBIP, and also reset when ascending.
Edit: That last message also needs to remove a peppermint parasol from inventory.