I finally got this to work. I received a ton of incorrect information about there being latches and hooks in the visor cap that were holding it in place. Here is the real deal after a month of frustration trying to figure out how to get the cap off without removing the headliner.

The visor cap is simply held in place by friction by two pegs that fit inside the lower assembly which contains the clip. Here is the key. Use a screwdriver or other tool to pull "straight down" on the cap. Do not follow other suggestions of trying to insert a screwdriver behind the assembly to unhook the latch and pull it toward you. No such latch exists. Just pull straight down on the cap and it will come right off.