I just got out my copy of Hanson's Firearms of the Fur Trade, to have a look at the De Witt Bailey data on these contract guns.
Common guns (like the ones pictured), chief's guns, rifles and pistols were supplied. In another thread in this forum, there was discussion of a rather nice chief's gun which appeared in an Ontario auction. The survival rate of chief's guns seems to be greater than that of the common guns. They are stylish sporting guns, and I think that they were more appreciated at the time.
I can only recall seeing one rifle turn up, and that was in the '60s.. The pistols appear from time to time. Not unusual to see them in original flintlock. I suspect that they weren't as widely distributed, and survived as curios, being less useful than the long guns. Maybe they were held in stores unissued, and eventually sold off after the flint period had passed.
I assume that the I/l\D brand was to provide permanent and obvious identification and to discourage sale.
There was a write-up of the Tecumseh gun in Muzzle Blasts some years ago. Chap had made a replica. This gun was also branded, and was no doubt government supplied.
For militia/irregular use, I do not think that these guns were supplied only to Indians, but also to European settlers.