Is what the questioner did—removing food from his mouth after remembering he was fasting and feigning chewing in front of his neighbor—considered forbidden and does it affect the validity of his fasting for the expiation of accidental killing?

There is no blame upon you for what you did with your neighbor by concealing your fasting for a beneficial reason. There is no legal prohibition in moving your jaw; rather, it falls under the category of permitted equivocations in Islamic law. This does not affect the validity of your fast because you did not eat or drink. Even if some food were to enter your stomach unintentionally, it would not affect the validity of your fast due to forgetfulness.