Re: Simple solution.
"He could walk out and find somewhere with free WiFi."
According to press reports he has a mobile phone. No doubt he can use that for WiFi. This is likely Ecuador just pretending to care so as to maintain good UK relations. Or if he goes on the balcony likely there are public services available.
"he could end up being extradited to the United States, where he fears facing the death penalty "
Not from anywhere in the EU he doesn't. Extradition is not allowed if there is any prospect of capital punishment by the human rights act.
The UK should just end this mess by guaranteeing safe passage - say by recognising him as an Ecuadorian diplomat after he faces court for skipping bail. He would probably only get a suspended sentence anyway. According to the Sentencing Guidelines Council, jail sentences should only be used for skipping bail when there are serious aggravating factors.