Part 18 is the tube that is stuck in the exchanger.
Have you removed the rear head yet ? After 24 years in place, I had mine apart for cleaning recently and everything came apart without any resistance. There's nothing in there for it to catch on.
The interior of the tubes (raw water side) can be nicely cleaned with a .22 rifle barrel brush. The outside of the tubes can only be cleaned by flushing the engine with a cleaner. Sorry I don't have a name for a cleaner but if I were looking at cleaning my AF cooling system, I'd look at Prestone cleaner :
They make the antifreeze I buy so they should know what they're doing when it comes to a cleaner. I hope.
Be sure to coat the two large "O" rings at the HE heads with a non-petroleum grease (such as SuperLube) when assembling the heat exchanger. It helps them to seat in the correct location. Do not coat the interior gaskets or they'll slide around and possibly be in the wrong location when the head tightens.
After cleaning out your cooling system, when you finally fill your system with a 50/50 antifreeze mix, be sure to use only distilled water (from a drug store) to add to the concentrated antifreeze. No tap water. I'm pretty sure you're presently looking at precipitates from your tap water. the sludge feels greasy because the particles of precipitated minerals are microscopic in size.
Let us know how the HE removal goes.