Sorry if I was confusing. I'll try it a different way and hope this will clear it up.
There was no "Bayonet Drill Manual" in the British Army until after the AWI. Earlier Drill Manuals that were used up to and including the AWI only had a few "basic techniques" shown in the manuals and certainly nothing that could be called advanced training or bayonet fencing and especially not a martial art.
Now the British Army up through the AWI (and afterwards) was one heck of a lot further along in writing, publishing and documenting some of the smallest details of day to day Army life and more than anyone else in the colonies. Detailed Minutiae was kept in log books kept by Serjeants (with a nod to the period spelling) Company Officers, etc., etc. going all the way up through the chain of command. Yet it is very difficult to document any bayonet training beyond learning how to take up the poses/positions with the bayonet mounted musket in the Drill Manuals.
(NA's had nothing even remotely resembling this documentation, because most tribes/nations had no written language.)
The only documentation that seems to have survived for any kind of bayonet training in the British Army up through and including the AWI, was the very few "basic techniques" listed in available Drill Manuals. (I emphasize the use of the term "basic techniques" because that is what others described how NA Warriors used the Tomahawk.) These techniques were basically just how to hold the bayonet mounted musket at a charge position or when receiving an enemy bayonet charge or against enemy mounted troops. There is nothing in the Drill Manuals on blocking or parrying an enemy's thrust or other techniques of "bayonet fencing" to actually use the bayonet effectively in close combat.
Now as you mentioned, the British Army was known for being very effective with the Bayonet up through and including the AWI. Of course some of this in the early stages of the war was due to the discipline of the British Soldiers and the fact that many Patriots did not have bayonets. However after Valley Forge when the Patriots were far better trained and disciplined for only a few months and had bayonets by that time, the Patriots did much better at going head to head with the British Soldiers and their bayonets.
Now what this tells me is that even with the British Army being what is often referred to as the most professional Army in the world at the time and with ALL the full time training they had received before coming over and training by their Senior Enlisted and Officers; they only knew a few "basic techniques" of bayonet fighting. Otherwise, the British would have easily won over the Valley Forge trained Patriots (even with their bayonets) in hand to hand fighting with bayonets at the Battle of Monmouth in June 1778. This because that battle was only a few months after Von Steuben showed up to begin to train the American Army at Valley Forge on 23 February 1778.
IOW, even the most Professional Army in the World at that time with writing, publications, manuals and a full time Army; only had a few "basic techniques" for bayonet fighting that can be documented. Of course the British Army was primarily trained in drill, movement and firing - with the bayonet only being a secondary weapon, though an important one. But, they did not have advanced bayonet techniques and certainly no martial art with the bayonet.
OK, a little more comparison between the Most Professional Army in the World compared to NA's. Yes, NA's primarily used guns or bows if they did not have guns and the tomahawk was their secondary weapon. But some state the NA's had no "martial art" with the tomahawk. Well, no kidding, but we also have to remember the British Army did not have a martial art with the bayonet and they had all the advantages over the NA's mentioned here and that some others have already mentioned.
What I'm getting at is why must we assume that the NA's had to have a martial art, written language, publications, etc., etc. to effectively use the tomahawk; when even the British Army did not have a bayonet martial art or bayonet fencing training in the period?
The British Army only had "a few basic techniques" with the bayonet, yet they used the bayonet pretty effectively. The American Army only had a "few basic techniques" with the Bayonet and not as much discipline and training as the British Army, yet they did well against the British in hand to hand combat only months after Von Steuben showed up to train them.
So "few basic techniques" with the tomahawk and taught to NA's by other NA's with more experience in warfare, made them fairly formidable along with their other tactics.
Gus