Was there any reasonable way for Jervis Bay to damage Admiral Scheer enough for the Royal Navy to finish her?
Short answerYes, if the armed merchant cruiser had carried torpedoes and reached a close enough firing position before being sunk.
NotesTorpedoes might have allowed Jervis Bay to damage Admiral Scheer sufficiently for other Royal Navy forces to finish her. The opportunity would depend on the auxiliary reaching a useful firing position before being sunk. In the related encounter with Scharnhorst and Gneisenau, the proposed close-range torpedo spreads could have destroyed both raiders while the armed merchant cruiser was also lost. That counterfactual rests on the ships being close enough that the torpedoes could not be avoided. Such a loss could make Hitler unwilling to authorize further surface-raider sorties.