I don't have any good advice on getting this out. The piston does need to be kept square with the barrel as it comes out so it is sliding only on the seal. Coat hanger likely has too much flex to do this. I would check with a hydraulic shop, sure they have run into this before.
Look inside the barrel for any sign of scratching or galling, it there is the barrel may not be reusable and require a new complete cylinder. Cost of barrel is close to 75% of complete cylinder add in cost of piston, nut, and seal kit it could be more than a complete new cylinder.