Logistics wins wars. With exception of WW1 and WW2, soldiers didn't really die in large numbers to the enemy. Soldiers died to the cold, to disease, and deserted due to lack of food / supplies / morale.
There are occasional exceptions where large numbers of soldiers died in battle... but those exceptions become remembered for centuries. It certainly wasn't a regular event (except in WW1 / WW2, which truly were horrific).
..with a lever action, effectively fighting a US army lead by battle hardened civil war veterans.
The natives weren't military slouches. What they lacked was the population and material resources to field fighting forces that could go toe to toe with the Europeans.
As a strategy, you could do a lot worse than Liberty ships and a lot of Russians.
But I know that Medieval English Longbowmen were only given something like 6 arrows per battle. And even that was enough to stretch the capacities of Medieval Britain's supply chain. 10,000 Longbowmen x 6 arrows is 60,000 arrows per battle.
IIRC, it was said that during wars, there wasn't any gooses or ducks to be found in all of Britain. They've all been killed, and their feathers plucked for the war arrows.
IIRC records for Henry in the Tower of London show a total of 3/4 Million arrows paid for and collected for the invasion that lead to Agincourt. With an estimated 5,000 archers at Agincourt.
Modern reconstructions show about 6 arrows per minute - and again IIRC ten minutes of volley fire against the French lines - something like 60 arrows per archer, or around 300,000 arrows. Even in plate armour that shits gonna hurt.
This is absolutely what happened to the Incan empire predatory to its subjugation to a few hundred conquistadors led by Francisco Pizarro. For those interested check out Last Days of the Incas.
I don't know how you get there. I'm pretty sure diseases went ahead of the colonists in many cases and wiped out entire civilizations before the colonists ever made contact. Even if it didn't wipe out literally everyone, it would have significantly destabilized or collapsed all significant political or economic systems.
Relatively speaking, any advantages of guns versus bows and arrows seem small. If I were inclined to make arguments about military technology, I'd speculate that plate armor and horses were more significant advantages than guns, but all of these pale in comparison to contagion.