Nice one, stales!
Your explanation sounds very reasonable, although I had been led to believe that it came from the Lancashire and Yorkshire textile mills.

Most mills would produce just one type of cloth, and the looms would be set up to produce just that. If there was an order for something special and different, a loom or looms would have to be set up differently.
So the usual product was what was normally set up to "run" through the mill. A special cloth might well be referred to as, "This stuff an't jus' t'roon o't mill, lad!"

And a reagent, Jackie, is something that reacts with other things - often an acid or alkali, I think
(Rhuby, GCE "O" Level Chemistry [failed])