My only remark here is that, AFAIR, it's not proper to name the French Army at Austerlitz a Grand Armee simpy because
the Grand Armee was the Army collected by Napoleon specifically for Russian campaign in 1812. So the Army Napoleon presented at Austerlits was just the French Army.
Concerning Kutuzov's plan - yes, it might be defensive but it had never been adopted, and it was just Leon Tolstoy's PR in support of Kutuzov's genius in his "War & Peace" where general-field marshal, count Mikhail Golenischev-Kutuzov (he had double surname, BTW) predicted ruining Weiroter's plan and thus an allied defeat and and it has little historical evidence. So, I personally cannot judge with full certainty what would Kutuzov have done shoud he planned the whole batte by his own. Don't also forget that it wasKutuzov who formally commanded the Allied Army meanwhile Weiroter planned the battle. So the one man delivered the plan and the other man tried to bring it into effect, or at least pretended to do that. Knowing ambitions of Old Sneaky Fox Kutuzov, I suspect that he might have sabotaged some aspects of the plan to show its disadvantages and he didn't much care how many sodiers would be killed in his doing so.