You could be playing.
Which came first, the phoenix or the flame?
I would also recommend teaching the game without the timed accusations phase.
Freeform debating the suspects seems to work fine.
Many groups prefer this way.
When I play these days I generally give a group discussion period of about 30seconds/player after the final bullet is placed.
I only enforce individual presentations if some noisy players are downing out quieter ones as everyone should have a chance to have their ideas heard.
Different groups prefer different presentation styles. As long as everyone is having fun, you are doing it right.
Grey Fox Games