Two things are conveniently omitted from your parable. First, the responsibility bourn by the fatty, for knowingly entering the cave with great difficulty despite knowing the same issue would arise during a time-limited egress...and then staying until close to time to leave; those decisions placed the group in danger purely to benefit his sense of curiosity. Consequently, the universal principal may be stated more narrowly and thus escape Kant’s argument: an life may be ended by an otherwise innocent person or group as the sole means of escape from an assuredly fatal trap knowingly created and aggravated by the owner of the life without sufficient cause.
Second, as a post-script, this (“Had I persisted, they may have also taken my life and
still killed Scott to save their own. There was truly nothing I could have done
to save him.”

doesn’t gibe with the milquetoast’s earlier willingness to actively end two innocent lives as well as her own simply to assuage her conscience. If she was willing to die and kill to avoid killing, then she should have been willing to resist to the point of forcing her friends to kill her even if the
likely outcome was merely her death occurring moments before the fatty’s (perhaps they could have used her dead weight to tamp the charge). It might have delayed them long enough for the fatty to live; it might have forced them to have second thoughts; it might have resulted in her unlikely success.