I don't think it's possible, not this way at least.
Regardless of the truth on accusations against Leo III (that seem to be doubtful, at best) they were the result of roman policies with one aristocratic faction (tied or lead by Theodorii, whom Hadrianus, the previous pope, was part of) trying to kill or chase Leo III.
Leo III was clearly the candidate of Franks, and Charlemagne supported him politically, economically (part of the loot of eastern raids was given to him) at the cost of papal autonomy : the role of the pope was to be subversiant to him including religiously (while Adrian made theological initiatives).
Charlemagne wasn't going to welcome a roman faction supporting a family that if proven tied and useful to Franks, wasn't nearly as managable and controllable by them.
Furthermore, attacking Leo III (in carolingian conception where the king was the leader of Christiendom) was attacking the king by refusing his justice and rulership.
I don't think mercy that guided his hand there (I concede it may have played, but not decisively), as it makes really sense politically for Charlemagne in order to make his rule including in religious sphere unopposed and mirroring his temporal rule (after all, if we can rid of a pope like that, maybe they could think to do the same for the king?).
If you want to get rid of Leo III, you need Carolingians to be really nerfed. Problem is, in 795, their rule was pretty well established in western Christiendom, and only an earlier death of Charlemagne could weaken frankish hegemony by breaking Carolingia (less importantly than in 843, Francia proper keeping a large hegemony over Aquitaine and/or Italy).
While a death of Charlemagne would fail to fill the OP, it would be the best chance to have half of it fulfilled.