No matter when, it's going to be spun as taking back power from an insane President. And it might be exactly that - since Thande is not wrong in saying that the modern US military has pretty much all of the benefits of running the country without many of the responsibilities. However, there's a recent potential victim I suspect you should look at closer: Reagan.
I don't think words can really convey the feelings among the top military brass during the early 80s. Vietnam had taken what was probably the finest military establishment in the world and shattered it. It had exposed the army to contempt and ridicule from civilians. Army officers believed this was something civilian politicians had done to them. And they were resolved to never let it happen again. Despite being pro-military and prior service himself, all Reagan has to do is seriously threaten to embroil us in another low-intensity conflict, or have one of his short, sharp interventions go unaccountably pear-shaped, and he could be removed.
I don't think this is likely DURING Vietnam. So long as the war is still going on, the officers tend to believe it can be won. They aren't going to turn on their civilian oversight while they have an active operation to attend to.
Would the military set up one of their own as an interim ruler? I sort of doubt it, unless Haig is somehow tangled up in it. GHWB will be installed, as everyone agrees is proper. Of course, he'll have a precedent to sweat over, and the appearance of complicity.