Head Teacher here!
I would try to help you BUT as the leader of a school (and not an officer of the law) like you, I have no 'power' to make it happen.
I won't be asking a TA (as suggested up thread) to stand outside; she has a job description; it doesn't include traffic duties; she is actively engaged, as she should be, in supporting children to learn.
I could stand outside, but I have a school to run; a focus on your children making progress.
Sometimes, however, I do find myself standing outside of school, in the car park because the same set of arrogant parents that park in your car park also park in the school car park. They block staff cars ( who, not surprisingly need to park their cars to be able to teach).
Occasionally they 'bump' into our school children ( health and safety report to write, lodge and investigate).
They always leave the school gates open after them (safeguarding issue - report to write).
As they turn into the school car park, they stop on the driveway so that when I turn right in to the school car park I am sitting across the main road in full traffic flow. This is to let their 'little darling' out of the car right at the school door.
Oh, and of course, long term parking; leaving their ( unknown to us) car for a week, in the school car park and causing a near security scare (2 hours of telephone calls to the LA & police, a police visit, safeguarding report to write and an investigation by governors).
My weekly newsletter 'name and shame/plea about child safety' doesn't work for the school car park. I don't expect it will work for yours.
( all rather tongue in cheek, but very true 😇😉)