It's definitely the Carbon Brushes. I'm an expert. I promise you that you can fix this problem yourself. A model L is simple to get into. After you remove the switch cover screw and cover plate, you'll notice two screws holding the back housing on. One is under the plate you just removed, and one is at the bottom between the rear wheels. Once the back cover is removed, just unplug the motor wires from the switch (Mark them in different colors so you know where they go for replacement). Remove the three screws that hold the motor plate to the housing, and pull the motor out.
Now, remove the two screws, one on either side, that hold the carbon brush and spring into the holder. It's on the side of the holder, which is sticking out from the motor on either side. The problem is one of only three things. The brushes are sticking from dirt in the brush housing. Or, the carbon brush is worn down almost to the spring (it's an inch long when new). Or, the commutator has either a burned segment, or has a deep groove worn in where the carbon brushes touch on either side.
By removing the carbon brushes, you can judge how worn they are. You can look at the brass commutator, to judge how deeply a groove has been worn. The carbon brushes have a spark at every segment of the commutator, and it's at 1400 degrees. But it's a small spark, and normal on any carbon brush motor.
Most likely, the brushes are sticking in their holder because of dirt buildup combined with carbon dust given off by the brushes. By removing them and cleaning both them and the brush shunt, if they're long enough, you might have solved your problem. Bear in mind that is a 40 to 50 year old machine if it's white or brown, At least 35 if it's blue. There is always the likelihood that the armature is burning out at the commutator. That's not uncommon for a machine this old.
By cleaning the carbon brushes you have, you might have solved the problem, and it can't hurt to try. There is one ball bearing and sleeve bearing in that motor. If it growls on the wind down, it's the ball bearing. If it vibrates, it's dirt in the fans. These are really very simple motors. If you have questions, just ask.