Thinking more about it, can the process simply be explained as:
Looking for an Amex CLI?
1) Have you asked for and received a CLI on ANY Amex-issued card in the last 181 days? If so, you have to wait until 181 days have passed.
2) Have you been denied a CLI (for any reason except for applying too early) on ANY Amex-issued card in the last 91 days? If so, you have to wait until 91 days have passed.
3) If the denial was for applying too early, the clock doesn't restart, but you have to wait for the original period (i.e. 181 from last approval, 91 days from the last real denial)
4) Otherwise, go for it!
Note 1: getting a NEW card doesn't count as getting a CLI, but all these rules apply to asking for a CLI on a new card
Note 2: Getting an auto-CLI (one you didn't ask for) doesn't reset the clock either.
