As far as crashing through like Billy be jiggers goes, that sounds a bit like what is known in modern doctrine as a penetration attack. Reno didn't have enough men for that, lack of sabers and saber mindset notwithstanding.
Reno became encircled in modern military parlance. In his day they would have said surrounded. And surrounded was what he was going to be no matter what. He simply did not have enough men for the size of force he was facing not to become surrounded, whether charging mounted or skirmishing dismounted. These days military leaders say OBE: Overcome By Events. Reno was OBE.
When Reno realized his predicament he did the only thing he could have done: he attacked. Reno didn't retreat, not initially anyway, he attacked. That's the nature of being encircled: any direction you go is going into the enemy. Reno was heard to say, "We've got to charge them!" And then he led it. And he led it with Bloody Knife's brains on his face.
The military operation known as a Breakout From Encirclement can be chaotic. This one was no exception. But Reno actually made a good decision and led by example at first.
But it does seem that things started to get strung out at about the river crossing. And then it seems to have become a mad scramble for the hilltop after that. Reno bears blame for this, of course, but there were others in the chain of command who didn't do any better. Reno wasn't the only leader there.