With two boys that went through Cub Scouts and as a den leader with a small workshop in the garage, I have quite a bit of experience with Pinewood Derby cars. I always made my boys do their own work, but I gave them guidance. My oldest son won the pack wide race once, but we usually lost only to the obviously Dad-made cars.
Definitely get as close to the weight limit as you can. When the car is at the top of the track, it has potential energy (PE). PE is proportional to both mass and height, so you want to get as much weight as high as possible, that is why everyone tries to get the most weight at the rear of the car. The idea is to get the car’s center of mass as high up as possible. One thing to watch out for here is that you don’t put so much weight behind the back axles that the front wheels lift off the track. It might be cool to see a car doing a wheelie down the track, but it usually results in the back of the car rubbing the track, losing a lot of the PE as friction.
The Conservation of Energy says that energy cannot be created nor destroyed, but it can be converted to some other form of energy. So that means, the car with the most PE at the top of the track has the best chance to win. The idea is to convert that PE to kinetic energy (KE). But friction is your enemy. With the small size of the cars, air resistance is almost negligible. Friction will be what kills you.
Where are you going to generate the most friction? In the wheels and axles - in most cases, the only moving parts on the car. Boys Life usually has adds where you can buy polished axles and balanced wheels and other stuff meant to reduce friction between the wheels and axles. The rules my pack used said that we could only use the part provided in the official BSA kit.
I would mount each axle in the drill press and have the boys use a fine file to smooth out the shaft of each axle and reduce the head to only as large as it needed to be. Then I would have them use a strip of 800 grit sandpaper and polish the axle and the inside of the head. If you have any polishing compound, you can get those axles to a mirror finish. I preferred the graphite over the teflon for lubing the axles before races. I would also have the boys use the fine grit sandpaper to take off any molding lines from the outside of the wheel and polish them up as well. There are also contraptions you can buy that will the insides of the wheels as well.
Per our pack rules, we didn’t need to use the axle slots provided but we had to have the same distance between axles, so I would drill different holes. I would drill them on a bit of an angle so with the weight of the car, the wheels were pushed to the outside so they wouldn’t rub against the car. I did this part since Cub Scouts aren’t allowed to use power tools.
The way the pinewood derby tracks work, is it uses a thin board that runs between the wheels - under the car - all the way down the track. So you need to make sure that the belly of the car is high enough to not rub on the track. You also need to make sure that the tires are absolutely square, so the car travels straight down the track without rubbing the wheels against the raised board. To check this, once the car is finished, find a long board and lay it on the floor. Put the car on one end and slowly raise that end off the floor. The car should travel straight down the board. You will need to adjust the wheels if the car veers off of a straight line.
Also, I would have my sons raise one of the front wheels off the track just barely. It was low enough to catch the track of it started to veer for whatever reason, but since it didn’t touch the track, there was no friction generated on that wheel.
Finally, our pack allowed us to add graphite between races. Get as much graphite between each wheel and axle as possible and run the car across the floor a couple times to breakup any chunks.