i've gotten really good results using a homemade headset press tool to help remove super stuck fixed bottom bracket cups. its the one made of 18" of threaded rod with two big washers and nuts (two plumbers reducing couplers optional) costs about 5.00 in parts at the hardware store and works beautifully.

get everything pulled off the frame except the fixed BB cup. spray some PB Blaster / liquid wrench if it looks corroded. keep one nut and washer on the threaded rod on the side where the adjustable cup used to be. the big washer should be up against the bare frame BB with the nut on the outside. push the open end of the threaded rod through the hole of the fixed BB cup and add the park tool fixed cup tool that fits and then add the other big washer and nut. tighten it down slightly past finger tight enough to hold the tool on the fixed cup so there's no potential to slip. get a good angle on the tool so you can put your body weight on it. you can also alternately sit on the floor holding the frame and push with your foot on the tool using your leg strength.

i've rebuilt about a dozen 25 - 30 years old bikes and it hasn't failed me yet.