I'm not a gifted passer, but when I make a move, if I'm not side by side at braking marker I watch the other car carefully and back out when neccesary. When being challenged, and there is any question of how close my rival is, I leave enough room for both of us to make the corner.
Things to try:
Instant look (Options>View>Instant Look>Instant)
Moving your overhead mirror to center/top on each individual car. (While in car. Options>View>Mirror Offset Lateral and Mirror Offset Vertical)
Virtual mirror on formulas. (Options>Display>Mirror Mode>Virtual)
Practice "looking". It gets easier as time goes on.
Race online a lot.
Find a group of racers that you like, race with them a lot, learn thier styles.
See if you like 'Look Function'. It can help in certain situations, but does take a little bit of 'feel' from the car. (Options>View>Look Function)
Sounds to me like you're on the right track.