Steve- A couple more 'food for thought' to help getting the most restful sleep prior to your walk with your options: 1) If you want to get out of the car and have fewer/no interuptions- The forest service lands just outside the south entrance is a good option. If you go farther back in, you'll have less traffic noise; a little rise will block the noise/light. After 9pm most of the vehicle traffic leaving or going into the the park is minimal.

If you want to sleep in the car; then you may want to go down to Grand View Trailhead. Its located farther away from East Rim Drive so it will be quieter from vehicle traffic than the S. Kaibab picnic lot option. After dark the only car traffic in the lot would be late exiters(which you can count on one hand and have 2-3 fingers left.) It is about 8 miles further east; and has a section for overnight parking. Downside is a longer drive; upside its a lot quieter.

Bright Angel Trailhead and Backcountry Parking Lot will be the noisest. Shuttle busses run right by them until 10:30ish. And there is a hotel/resturant in close proximity to both; so it wouldn't get 'canyon quiet' until after the bar closes.

The BA trailhead parking AND the S. Kaibab Parking lots probably will have R2R foot and car traffic at all hours.

A note on Stealth Camping inside the park: Camping inside the park, in an area not designated for camping; is not allowed. Is it done? yes.

Car sleepers at trailheads usually are not ticketed; as long as the occupants of the vehicle are quiet and not bringing attention to themselves-noise, items outside the car, etc. The only downside would be if a Ranger patrol spotted a body(You) in a car and did a 'courtesy check' to ensure you weren't dead or in need of medical aid because of finishing a R2R, etc. Grand Canyon annually averages 12 hikers dying below the rim,and 2-3 suicides a year; so this isn't 'Ranger Hasseling'.

Someone who sets up in the pines and isn't taking a break; will more than likely get a ticket for 'camping out of bounds' and then have to move; provided they are seen or brought to the attention of the rangers; ie setting up a tent/bivy/ sleeping bag in close proximity to the S. Kaibab Picnic parking lot that could be seen by a patrol. And this being a busy spring R2R hiker time; there will be more Ranger LE patrols/hiker aid responses to the S. Kaibab trailhead area. (This is why I've been leading you away from this option.Don't need the extra expense of a ticket and losing sleep due to having to get up and move..)

I may want to take an early morning walk that Friday morning; and could save you the taxi fee- More on this option as we get closer to May.