Some thoughts.
As far as the mechanism slowing down and stopping is replace the drive line cord.
I have found after after years of use the cord/string becomes too 'smooth' to get a good grip on the pulley. Replacing it will solve that problem. Also bend a piece of sandpaper in half and sand the groove the string rides in the drive pulley. This will give some bite in the nylon plastic.
As far as the grappler not moving far enough to drop the culvert squarely in the car, remove the single screw that holds the building to the frame and move the building about 1/32 of a inch towards the track. Hold with your hand and try operating the loader. Drill a small hole and remount the building if this helps
Be sure the culvert ramp is tight against the building. Add shim of cardboard if necessary. Move track in the channel as close to the building as possible.
If all the above fails, You can send it to me for repair.
Chuck