While checking KMC for recommendations be sure to compare the US and UK sites. They differ somewhat and the UK site offers more explicit and readily accessible info on chain maintenance. I doubt the two nations disagree. It's just that KMC websites have always been a disorganized mess.

The UK version of KMC sites does indeed recommend sticking with the factory lube and not stripping it out. I can't find the same info page on the current US version.

I usually don't strip old or factory lube. I just wipe down the chain with alcohol or Goo Gone on a paper towel, then soak the chain overnight in a crock pot with wax. Occasionally I'll spoon off the residue that floats to the top. I figure the heat and wax need time to penetrate and eventually displace the original lube. Dunno, just guessing, works for me and reduces time wasted on messing with chains rather than riding.

And crock pots don't take long to heat up. I use a Little Dipper. Came free with my big Rival crock pot. The Little Dipper will liquefy Gulf wax in 30 minutes. When I'm thinking about monthly chain maintenance chores I'll plug in the crock pot. It'll be ready by the time I have the chains off the bikes.

Using any other form of heat -- especially open flame gas ranges or even electric -- demands more attention. Setting the flame is guesswork. And electric ranges with open coils have terrible thermostats. You need a pot made of heavy, thick metal -- cast iron or those heat dispersing discs for aluminum and/or copper -- to get reasonably consistent heat.

Get a Little Dipper crock pot, or any comparable smaller crock pot from the thrift store for a buck or two. It's much easier.