hi Mr. Dane,
if i have to tackle this problem these are things i would consider.
if you can isolate some of this material i suggest you do a burn test on it with a butane lighter
natural fibers will usually burn to dry ash when you smear it between your fingers, and artificial fibers will melt.
this test is used in textile industry to detect silk and cotton blends, pure silk and cotton burns to dry ash with no melting.
draino will not harm any of the original engine parts however it will be ineffective against any artificial plastic based fibers
so if your fibers melt you can skip trying draino as it's already a no go.
pure gasoline may melt some plastic fibers away, but then you will have to be a concerned about the water pump seals and lubrication.
acetone will absolutely damage nearly all plastics and rubbers, so if you are flushing only a radiator then that would be okay, but acetone will destroy your water pump.
acetone won't do much to natural fibers like silk or cotton.
i would not recommend any acids for this application as acids would be less effective than the aforementioned chemicals and the coolant system has parts that are susceptible to most of the usual candidate acids at various places.
-s