I think I have used CLR before with good results. Something recently surprised me how well it worked, but I can't remember if it was Wheel Cleaner, Aluminum Boat Brightener or Bathroom Mildew Cleaner. It was definitely something I usually having kicking around the shop utility sink.
Since I am doing full cooling system refresh, also want to clean out the coolant reservoir too.
Regarding your full cooling system refresh I was wondering if you decided to do anything more than a water or water/vinegar cleaning flush of the cooling system? I'm in the middle of addressing the system myself and thought to ask what you used.
Did mine with Mould/Mildew bleach, didn't have any small enough hose end bungs, so I looped a piece of hose between upper & lower outlets so I could hang it up to soak & keep with all the crud submerged in bleach, came up better than expected.
Throw in a few stainless m4/m5 nut can't hurt to scuff the crud loose.
Central heating cleaner will shift it too, dunno if its aggressive to plastic tho?