I think the derivation is from a loose bundle of something. The Latin term "Facine" describes a bundle of sticks, held as a badge of office in ancient Rome to show they had authority over the citizens. This is where the term "Facist" comes from.
The term was also used to describe bundles of sticks used to form defensive structures as they would capture arrows and other projectiles, a sort of middle age sandbag. The term was also used in WW1 & 2 to describe bundles of sticks carried by tanks to fill in ditches.
Traditionally in UK,Faggots were bundles of twigs and brushwood used to fire a bread oven. They burned very quickly giving lots of heat and little ash. They were roughly made and of little value. This is where I suspect the connection with meat Faggots comes from, as they were also a bundle of cheap ingredients, roughly made..?
I suppose the association of bundles of sticks to hand rolled cigarettes could be made, although much of London slang is ryming, and I don't see one there..!
How the term became associated with homosexuality is more of a mystery...!
Still, I used to smoke fags and I do like a good Faggot and peas! What this is to do with musketry is less obvious, but perhaps someone could see if a Facine/Faggot would stop a musket ball?
..and yes, Haggis is Scottish, but is made from Sheeps pluck rather than Pigs..
'Fags' for cigarettes comes from the stubs left of brushwood used for kindling. Short stems which cigarettes resemble. Thus the 'fag end' of something. Cigarettes came to Britain from soldiers in the Peninsula campaign noticing that the peasants would wrap their tobacco in bits of paper which was far more convenient than the normal cigars and cheaper to boot.
Felix I envy you. I trust that there was a mug of strong tea to follow. Some sort of suet pudding and custard would fill in the odd spaces left.