The following information from Harold L. Peterson, Arms and Armor in Colonial America, 1526-1783 and M. L. Brown, Firearms in Colonial America: The Impact on History and Technology.
I want to quote from the two books referenced above first.
(Brown, p. 138)
Paper cartridges were employed in the English colonies of North America by 1650 and saw widespread use by 1675, and they were undoubtedly used in Spanish Florida by 1683, for Governor Cabrera then referred to cartridge pouches being distributed with flintlock ecopetas.
Paper cartridges did not supersede the powder flask or the powder horn employed in Colonial America since the fifteenth century, for each continued to serve a populace long accustomed to their use for hunting and militia duty and they were equally popular among the Native Americans who duplicated powder horns and made flasks from birch bark, tortoise shell, and other materials.
The leather cartridge box conveniently attached to the infantry belt or shoulder strap was introduced in colonial America with the appearance of paper cartridges. The cartridge box was known in New Sweden by 1654, for Governor Rising then described “bags of leather with three or four compartments, in which one could place cartridges; these are many times better in the woods than bandoliers.” In New Netherland the Dutch retained bandoliers for use with matchlock firearms and preferred the patron as a cavalry accouterment, while cartridge boxes were used with flintlock firearms.
(Peterson, pp. 62-66)
Despite their apparent advantages, bandoliers suffered from several serious defects which did much to undermine their popularity and make their period of popularity relatively short. Lord Orrery, one of the outstanding military writers of the 17th century, analyzed these shortcomings in detail:
Besides, I have often seen much prejudice in the use of bandoleers, which being worn in the belts for them, above the soldiers’ coats, are often apt to take fire, especially if the matchlock musket be used; and when they take fire, they commonly wound and often kill him that wears them, and those near him: for likely if one bandoleer take fire, all the rest do in that collar: they often tangle those which use them on service, when they have fired, and on falling off by the flanks of the files of the intervals, to get into the rear to charge again. To which I shall add, that in secret attempts in the night, their rattling often discovers the design, and enables the enemy to prevent it; and in the day time on service, especially if the weather be windy, their rattling too frequently hinders the soldiers from hearing, and consequently obeying the officer’s word of command, which must be fatal when it happens…
The device that appeared to supplant the bandolier in America after less than half a century of popularity was the paper cartridge. This innovation was developed in Europe sometime during the second half of the 16th century. The first cartridges were simply individual charges of powder rolled in paper tubes. The balls were still carried in the pouch. They were, thus, a true form of semi-fixed ammunition. By the end of the century, however, a means of attaching the ball had been devised. This was done by tying one end of the paper tube to the sprue which was left when the ball was cast or to a special flange which was sometimes added to the ball. In neither of these instances was the ball covered by the paper, but now a form or fixed ammunition had been developed. It is not known just when the completely wrapped cartridge was developed, but as late as 1697 Saint Remy illustrated a cartridge with the ball attached by its sprue as the latest type.
…The exact date at which cartridges were first brought to America will never be known, but most of the references to them are found about the middle of the 17th century. The Dutch in New Amsterdam used bandoliers for their matchlocks but ordered cartridge boxes for their wheel lock and flint arms. In New England, Captain Church frequently referred to the use of cartridges in King Philip’s War, 1675-1677, and inventories of arms of that period in various individual colonies include cartridge boxes. It is safe, then, to assume that the cartridge was in widespread use in America by the third quarter of the 17th century.
It should not be supposed from the above comments that the bandolier completely superseded the flask and that the cartridge completely superseded the bandolier in the period under consideration. The flask and horn retained considerable popularity, especially for non-military use, throughout the entire period and indeed until the metallic cartridge made the muzzle loader completely obsolete. The bandolier enjoyed only a short period of popularity, but a few survived until almost 1700.
So, where does this leave us? We do know that ball was often carried separately from the powder. The powder would be carried in a flask (the European style with cut-off nozzle or a simple powder horn) and the ball in a separate bag or pocket, or a bandoleer with powder charge in bottles and ball in the bag at the end of the strap, or powder measured into a paper cartridge (no different than our reenacting blanks, called “squibs” at that time) with ball carried separately. When ball was part of the cartridge it seems the end of the paper tube was tied around the sprue of the ball. The ball inside the cartridge seems to have been more 18th century, at least according to these sources. We know that the Phips ship, Elizabeth and Mary (1690) had on board bandoleers, and three different styles of cartridge boxes, with ball present in at least two, and another box with just the paper wrapped powder charge (no ball).
Also note that, in 1689, when Church came on the battle erupting at what is now Portland, ME, he had casks of balls with him. They were brought on shore for the use of his men. It is highly unlikely they were going to laboriously make cartridges, especially tying the paper tube to the sprue of the ball. They most likely had flask/horns for the powder charge and the balls carried separately. In this event, the balls turned out to be musket balls and too big for most of the weapons carried by his Indian and English men, and they had to hammer them down to reduce the diameter. The point being that Church was carrying casks of powder and casks of balls, not premade cartridges.
For safety reasons, we cannot load directly from a flask or horn, so that method is out. Certainly, the use of cartridges for Church’s Co. is warranted, but we should consider simulating separate powder cartridge and ball whenever we do a demonstration.