Japan... LOL, sorry, I don't know where to purchase these motors. I imagine that you would have the best luck buying them from the dealer, or buying a similar scratch and dent machine.
I am not sure about silicone.
The bearings are usually "Ez-Glide" nylon coated sleve bearings, or traditional high grade steel and collar bearings, (Rare, those are the noisy ones.)
Stepper/servo motors are not like a normal motor. you tell them to go to a position, and they will exert as much force as is needed to get there. Normal motors have less power as they are further from thier push/pull source, and usualy require more care.
I am sure that a little dap of lube once in a while is fine, some people don't know what a "Little dap" is, and end up lubeing it up like a bike chain. (I say that you should just buy a can of compressed air from radio-shack, ones made for cleaning electronic components.)
You may be able to use a little alcohol on the end of a q-tip, to free up debris. Then follow that quick swab with a jet of air. The alcohol wil vaporize almost instantly. I think that the sleve bearings normaly prefer graphite lube when manufactured. Plastic is now manufactured with lube now inside it, it lubes as it wears, and is highly heat resistive.
I think that graphite lube uses water as the transfer medium, which will evaporate and leave the fine graphite powder behind.
NOTE: Don't assume it is a weak or dyeing motor until last... Try the other resolutions first, where possible.
One last unmentioned issue, (Major long shot here...) An underrated transformer which can not supply enough peak power may not be able to handle the higher demand that the servo motors are calling for. You can test for this by unplugging all the internal lights, sound and wait until you get the spin-up that starts one wheel at a time... That spin-up will "Wait" less, since each individual wheel is getting full power. As opposed to power divided by 3, as all three wheels try to spin up at once.
SOLUTION: You need a new, or higher rated transformer. (I don't reccomend doing that yourself, as it involves 120v wires to be connected to it.) You may have a 4amp when you need a 5 amp transformer... or a 3 amp when you need a 4amp transformer. You may also just need better ventalation, if this only occurs after an extended period of play time.