I don't know how official this is but I have used two different approaches
to the stiffened lubricant problem.
One is what you and Charles have been talking about which is to use usually a spray chlorinated hydrocarbon spray cleaner to cut and remove the old lubricants. Charles mentioned automotive cleaners. You have to be a bit careful in that aisle because many automotive cleaners are "carburator cleaners" and are essentially thin spray, paint removers. Very strong solvents likely to damage the plastic.
Products labeled brake cleaner or general cleaner degreaser are similar and could be used.
Xylene is an ingredient of carb cleaner and paint remover and is very strong and will cut almost anything. But most nylon gears could survive exposure to it. But I think I would reach for something weaker. Electronic spray cleaner is likely to be safer for plastics.
Then you relube with a lubricant labeled "Safe for use on plastics"
My favorite for this purpose is teflon based grease designed for use in high vacuum environments. It will never oxidize in my lifetime nor that of my grand kids. It is expensive and hard to find. It is not the best lubricant either. You want to figure out whether the viscosity of the lubricant will affect the operation of the unit being worked on, as for example course focusing dovetails and racks.
http://www.sandsmachine.com/grease_t.htm
Another approach is what I call freshening the lubricants. Greases are mixtures of oils and waxes and fats (and also soaps and emulsifiers) designed to have particular characteristics. When they age these different components may oxidize or polymerize or both. They dry up. Sometimes you can return to a reasonable facsimile of normal function by adding a lubricant. The first that would come to mind is WD40 which you really should not use except for cleaning. (It wont hurt nylon btw) Its not a very good lubricant and doesn't stay well. But there are similar products that have teflon dispersed in them and whose solvents are labeled as safe for plastics. They have names like TriFlow and TriFlon.
Another thing I use to soften up old grease is a drop or two of whale oil.
(which I found in an old engineering school storeroom labeled"Sperm Oil" and rescued from being tossed) Of course whale oil , which is how messers Nye got their start , making watch and clock oils out of whale oil, is not going to be terrrbly easy to find. However apparently a suitable substitute is found in jojoba oil which is very easy to find and inexpensive.
Sometimes just adding one of the above products and operating the gears to mix it will refresh the lubricants to the point where total cleaning and replacement may not be necessary.
Remember to make certain that nothing that goes on any optical gear can contain silicone oils. Be rigorous about this. Don't even let such products on your bench. Silicone oils spread continuously down to monolayers. They get into cemented lens elements and cause them to separate.
Changing the knob was very simple, first I removed the coarse focus knob with the three ph screws, then I needed a 1.5 mm hex key for the two set screws in the small brass ring, after loosening them, the rest of the old knob just slid off the shaft. The brass ring had a protrusion that connected it to the end of the plasic fine focus knob, so no glue needed in the reassembly to keep it from spinning or anything, just retighten the set screws in the ring and slide on the new knob and then tighten that down with the external nut.
. Beautifully smooth movement when finished.