I end up beating this drum every time Nappy's early period is brought up, but Murat says hello and would like to apply as that Counter-influence. He played a rather major role in the Revolutionary campaigns on the Rhine, and if his attacks into the Germanies to catch and defeat the Habsburg armies were more successful he could have returned a conquering hero with a loyal army well bought off with loot. That dosen't stop the government from being a ranshackled mess that's going to need to be replaced with a stabilizing authority sooner or later (including some way to peacefully demobalize the mass levee forces without them getting surely and using their guns to make demands, which is what vexed every civilian regeime as they could never catch up with the delayed pay owed to the men or get control of their system of supply), but at least you have different armies checking one another
Are you sure that you are talking about
Murat and not
Moreau?
Murat was promoted from the 2nd lieutenant to colonel only after he brought that guns on Bonaparte's order, after which he accompanied his general yo Egypt and then Italy and never played any major or even noticeable role in the Revolutionary campaigns on the Rhine or even during his later career distinguished himself as an independent commander or even demonstrated any strategic or administrative abilities (even administration of his cavalry troops was lousy in the terms of proper care about the horses and pretty much everything else outside a direct cavalry charge; quite a few authors commented on that).
Moreau, OTOH, had became
général de brigade in 1793,
général de division early in 1794, in 1795 became commander of Army of the Rhine-and-Moselle, commander of Army of Italy in 1799 and in 1800 was appointed commander of the Army of the Rhine in which capacity he won at
Hohenlinden. By that time he was considered the 2nd best general of the Republic with the distance from the 1st one not being too big.
The problem with him in OTL was that, while actively disliking Directorate he had no political ambitions and in OTL preferred to help Bonaparte in his coup. Make his characted different and you have your candidate.
So, if you are staging your alt-coup (

) , preferably between 21 May 1799 (when Nappy was forced to retreat from Acre) and August of 1799 (when he abandoned army and fled), by the time Nappy is reaching the French coast (or have his ship intercepted by the Brits and sunk with everybody abroad) Moreau is a head of a new government. Bonaparte is put on trial and either shot for abandoning his army or imprisoned or simply fired from army with or without a major scandal. I'd assume that Moreau's friend, Bernadotte, could influence him to make things quiet (Napoleon already managed to screw him both in Italy and in Paris but he was on good terms with his brother-in-law, Joseph Bonaparte). On a positive side, unlike Nappy, Moreau did not suffered from mania grandiose and seemingly liked to enjoy life which would make him a better candidate for an earlier peace arrangements.