First line on the maintenance information page of the manual says:-
"Regular maintenance is essential to a game's continuing contribution to the operators earnings." Emphasis on regular!
I guess if the grease is drying up to the extent that it is affecting game play then it's well and truly due for a service. Then as you say, pull it apart, clean with shellite or whatever, but then I believe, re-grease...sparingly! You don't need to see it oozing out everywhere, quite the opposite in fact, just a light smear to create a barrier between the metals, less is more as it helps to stop attracting dust. I personally would not apply any grease to plastic or fiber material that are in contact with metal, but metal rotating or sliding on metal, every time! Things move smoother and as a result have minimal wear and run quieter. Yes they will start to gum up over a couple of years but that's an easy fix. Gives you a chance to get your hands dirty and clean your pride and joy. Gosh even my ride-on lawn mower needs a grease and oil change. Thankfully it has a small LCD display to remind me when it's due every 25 hours. I don't have to wait until the wheels stop rolling or the steering is too hard to turn before I realize it needs a service. Just my five cents worth