Just top of the gear and chain cases YEARLY with the 00 grease from Tractor Supply. That is good quality 00 grease for cheap.
00 and 80-90w are completely different fluids. The viscosities are way different and so are the additive packages. Oils and greases are formulated for specific applications. Long story short, Snapper says to use 00 grease. Listen to what they are saying...
About the so called dried up 00 grease. I can promise you this, if you split the gear or chain cases, you will NOT find dust where the 00 grease has dried. That is some old internet BS. Dried up means that OVER TIME, their grease has leaked out and they never refilled with 00. Now stating that, yes oils and greases over time can become thicker, IF left open to the air directly. The solvents evaporate which thickens the fluid (years and years old fluid). So if your cases were split or the fill plugs were gone from the machine, I could see some thickening. Don't over think this. Top off with 00 and never look back.
Now if you want to be thorough, remove the cases and split them. Clean them out with the best greasy oily parts cleaner on Earth. It's called Diesel fuel. Use an old metal paint tray and an old paint brush. Diesel is cheap, what $2.75 a gallon compared to canned death (brake cleaner) with all its deadly fumes and high prices. Diesel is a great parts cleaner EVERYONE forgets about. Clean the carbs and push mower transmissions out with it.
slomo