In addition to the $333 distribution from the Roth IRA not being taxable, it will also not be subject to penalty.
"If I were eligible for Roth contribution in 2016, would there be another way to fix this by reallocating that contribution to the 2017 year and avoid the 2016 penalty?"
Yes, if you were eligible for a $333 Roth contribution for 2016 and had you already contributed the maximum traditional IRA contribution for 2016, you could obtain a return of contribution of $333 of the traditional IRA contribution for 2016 before the due date of your 2016 tax return and then allocate the $333 of excess Roth IRA contribution as a 2016 Roth IRA contribution. But since you are not eligible for a Roth IRA contribution for 2016, that's not an option.
All of the necessary information is contained in Form 5329, Form 8606, and the instructions for each. It just takes a bit of combining bits and pieces of information from each to reach the correct conclusions. It seems that you actually did bring that information together (except for thinking that the distribution from the Roth IRA will be subject penalty).
