Sounds good, except that while it would work for pressing cups in, how are you going to get the parts behind the cups to press out?

Try this.
Step one figure a way to rigidly support the BB shell by the rim so all your hammering energy goes into moving the cup, instead of being dissipated by flex.
Step two look for a decent piece of thick flat scrap steel that you can feed between the cups and lay across the lower one like a bridge.
Step three find a large diameter bolt or hunk of scrap to use as a punch, and using a serious hammer like a 4# mallet deliver a no BS solid blow to knock it out. Multiple smaller blows will only distort it, whereas one big blow will break it loose. (wear protection, especially eye protection)

If you have access to a press like an automotive bearing press follow the same steps but use the press in lieu of the hammer.