Then, you simply raised too little. I always thought that raising an angel round means "finally to be able to focus 100% on the start up". I'm not sure whether your investor would like it, if you spend your time doing other stuff than making this startup big (I sure wouldn't).
However you might not be able to wish more funding into existence. In that situation, the approach "we've got X money and we need Y runway so we're going to adjust our salaries accordingly" seems sensible. As per my other comment, totally agree that part time work is unlikely to be a good solution.
