I think you misread what I wrote. I suggested that my funds would sit a special address from which they could only be spent with signatures from all (or at least the majority) of my "semi-trusted 3rd parties". If one of the "semi-trusted 3rd parties" refused to sign my transaction, every node in the network would reject it. No hashing power needed.

This feature would already be feasible today without changing the existing protocol. However, it puts the user at the risk to lose their coins if one of the "semi-trusted 3rd parties" just refuses their signature, disappears or has trouble with their internet connection. Keep in mind that any of my ST3P can block my transactions, so the chance that my coins get frozen because of a dead ST3P is higher than the chance that a particular e-wallet service disappears. In order to mitigate this risk, we would need the option to perform an exit transaction and that would require a change to the protocol.

Btw, I don't really like the term "semi-trusted 3rd party". Does someone have a suggestion for a synonym?