Patience and every tool in your toolbox is the answer
THEN, smash it out with a club hammer
Had the same problem last year, tried all of the above - bolting tools on, vice, drifts, punches, blow torch, etc, etc. But I ran out of teeth or anything else to grip onto on the cups, last resort was to smash it out using a club hammer by supporting the BB on the vice jaws (the plastic side melted and I dug it out and wacked the axle from the drive side) but this was an early 90's saracen steel frame that will still be intact when the earth is a nuclear wasteland
probably not recommended this way if you have a aluminium frame though?
The BB body eventually cracked, it had sort of rust-welded itself to the BB shell, the the alloy cup just sort of bent as the axle slowly pushed the whole lot out, had the threads chased at lbs and all's well now.
Pic of the offending item:
I was nearly in tears though as I took the hammer to it, so good luck and hope you don't have to do the 'last resort'
Then one day you find, 10 years have got behind you ....