Fiten, go ahead with the servo swap. The 2055 is Traxxas version of a high torque servo. Supposed to be about 70 oz's. Those big tires and 4wd need more than that. "all you can get" is how to approach this issue. 5 and 6 year olds driving it... with metal gears is recommended.
The "main" or "spur gear" runs on a "slipper clutch" and floats on hard rubber pegs. The run out "warp" you see is normal. Don't let this bother you. Also since these gears are injection molded you will find that every single one of them runs out. Some are worse then others.
When you opened the box, did you connect the blue wire to the glow plug? This wire has to be connected for the glow driver to work. If so, did you have a roll over? If you did, that can cause the wires inside the wire insulation to partly break. Since the truck ends up on its roof, the wire gets pinched. It is common to have to replace this wire often, depending on your driving habits . Other wise you have a problem with the hand held starting box.
Surprised you didn't have trouble getting it started since Traxxas dumps about 2 oz's of oil into the air filter. Take the foam element out and put into a paper towel and squeeze out the excess oil. I have also found that whatever kind of oil they use seems to screw up the glow plug if it gets into the combustion chamber.
The transmission takes time to loosen up. It's common for them to not want to shift from forward to reverse when new. You are correct on the idle speed. The engine will develop a better idle once it's broken in. You might have to adjust the carb barrel stop for a lower idle speed, after giving some time for things to loosen up.
Other than that, its just fix the broken parts. That will be body posts, front bumper, front bumper mounts, front bulk heads....hehe
Have fun.