Ahhhhh! A clean transmission is always appreciated by changing gears!
Glad this solved many of your shifting issues.
I wonder if the "skating" could be solved by a new chain? You don't mention what brand or speed chain you are currently using (at least I couldn't find this with the search function). I did see where you speculate that it would be best to stick to a 9 speed or lower chain. It would seem to me that if you are using 10 and 11 speed sprockets, a matched chain would be essential to better shifting performance. I'm with you that I wouldn't want to shell out the $$$ for an 11 speed chain. But consider trying a new 9 or 10 speed SRAM or KMC chain.
Or, remove and clean your current chain. This is how I clean my chains: Remove and wipe thoroughly with a WD40 soaked rag. Next, I scrub mine in hot soapy Dawn dish detergent, followed by 1/2 hour in the ultrasonic cleaner with a Branson MC-3/hot water degreaser solution. After a complete rinsing in hot water it goes in the oven at 200F for at least a 1/2 hour. As soon as I remove it from the oven I lube each link with warm ChainL oil.
I went ahead and deleted my post with the Sheldon Brown Gear Calculator Chart since it was incorrect. Best not to confuse folks with the wrong information.