[Mr Gazza]

David, It's far better to get the tank off and also the filler cap and internal rubber tubes.
The piano wire will just dig in the rubber and stop, or might even puncture it if you got angry enough!

Best to go in from the top as the wire is difficult to get round the 90 degree bend at the bottom. although I don't know if the plastic tanks are configured the same as the metal ones? Also you will displace the blockage to outside the tank rather than into it!

Regarding the Bilt Hamber Deox-C rust eater. I doubt very much it will have any effect on your plastic tank. It comes in a plastic bottle. It eats rust with a veracious appetite but very little else, including sound steel, although they do mention not to use it on plated steel, especially Zinc.

I used a needle on a syringe and so could get it right into the tube. I didn't spill very much at all into the tank that way. Easy to mop out after a little water was sloshed in and then finished off with clutch and brake cleaner which is hygroscopic.