The main chance for his to make any serious change in OTL would to attract interest of the Russians who were at that time operating on the Med, Ionian and Aegean Seas and in Greece (
Russo-Turkish War of 1768–1774) trying to ignite the Greek uprising against the Ottomans.
A reliable land base would be a factor in his favor and bellicose reputation of the Montenegrians could be another one.
However, few things had been against him. 1st, Catherine II (and as a result Alexei Orlov, "the theater commander") had fixation on Greece with a far reaching idea of recreating "Byzantine Empire" for Catherine's grandson, Constantine. Keeping this in mind, Montenegro was slightly too far to the North to be of an immediate strategic interest. 2nd, his claim to be Peter III made cooperation politically unfeasible for the Russian commanders (especially for Alexei Orlov who, besides being one of the leaders of the coup, had been "credited" with personally participating in the assassination of Peter III).
So, for him benefiting from the situation, we have to change few things. 1st, Catherine should be more open-minded about her goals. The Greeks could be enthusiastic but during the uprising they proved to be not very impressive soldiers. So if her goal was just create and maintain a persistent problem in Ottomans' rear (end) then Montenegro could become a 2nd best option which could be used even during the Greek uprising. This would definitely keep the Albanians busy. Of course, there are conditions for this plan to work. 1st, Šćepan's claim about his "true identity" should be ignored by the Russians and he himself would have to play it down; not very convenient but quite possible. 2nd, MUCH more difficult because it is related to personality of Alexei Orlov. He was an impressive and charismatic figure, a gifted statesman and his personal willpower had been critical in a decision to fight the Ottoman fleet at Chesma. However, he was not a capable or even experienced military commander and quite sybaritic. Plus, the whole Russian military force was simply inadequate.
So, if we assume (a) that Catherine's "Greek Plan" involves Montenegro at least as a distraction factor (for the Albanians) AND (b) she sends more troops (few thousands more) AND (c) there is a capable commander of the land forces (under Orlov's nominal command) then Montenegro can be turned into a meaningful theater of operations with a possible expansion of Šćepan's rule to at least part of Serbia. Or perhaps he could capture Dubrovnik (at that time Ottoman vassal).