You might find a Tange headset who's upper stack is close enough to allow the use of the pressed in cup. Or if you're willing to buy a headset at a bike shop, condition the purchase on the no charge switch of the top cup (only) in your frame, or maybe for the added cost of a beer. This should be an easy sale at a shop where the owner either does his own work, or knows how little you're asking.

Otherwise, here's how to DIY using my emergency field repair approach. You'll need to scrounge up a coin or disc of some sort, too big to fit through the cup, yet smaller than the head tube ID. File or grind two flats (like a racetrack oval) enough that you can slide it past the pressed in cup. Let it flop there, and drive it and the cup out using something like a cut-off broom handle.

You can drive the new cup in (usually) Using the threadless system like a screw jack (don't use the centering cone, or balls for this). If that doesn't work, start it as well as you can, support the lower cup on something by the inner area (not the lip of the cup) and use a block of wood as protection while you tap it in with a hammer.

No crisis if it doesn't seat 100%. Time and the normal pounding as you ride will finish the job over time, but you'll need to carry the 5mm hex key for regular adjustments until it's home.