I have a mid-drive with 2250 miles on it, and the chain...a KMC X10e...shows no wear. KMC makes a similar 9-speed chain, the X9e. I use Rock 'n' Roll Gold lubricant.
I still had chain drops on my 1st gen CC even with a shorter chain. What fixed this is getting a narrow wide chainring. The teeth are shaped so the chain only fits a specific way & the their profile keeps the chain from flopping from side to side. Look for "DECKAS Single Speed Chainring 130BCD MTB Bike Narrow Wide" on ebay.
You can get chain guards, I run an eBike chain from Connex/Whipperman. They won’t run on a narrow wide. Google YouTube for a chain drop video. Easy fix likely.
I didn't realize some chains wouldn't work. I use low mid tier KMC chains. The chainguard still fits with the thicker chainring on my CC, but maybe the CCS is different?