You are putting a final touch on this exercise.

If you consider in front of you to be twelve o’clock on a clock (analog,
not digital), then I want you to constantly scan at 11:00 and 1:00. This
widens your perception (peripheral vision) just enough that you see
things/people in advance of them passing by your side.
For me, 2:00 and 10:00 are too wide. I can’t see both sides at the
same time (pardon the pun). With a narrower scope, I can see both sides
at the same time, without shifting my head.
By adding this small touch, I can see everyone before they pass. It
cuts down on the amount of attention I have to give to protecting the sides.
It doesn’t eliminate it — it just “almost” kills two birds with one stone.
And there you have it. Practice moving someone through the crowds
for 20 minutes a day for a month, and you will see marked improvements.
for some, it will take longer to become proficient. You really want to get
this down pat.