I had Chase Amazon for four years without a single auto-CLI. I wasn't about to ask them for a CLI because I was afraid the same thing would happen to me that's happened to others here, take an HP and get a lousy $500 or something.
What I eventually did was app for the Freedom when my score was at its highest and my util pretty low. I got approved for a decent limit, then moved the Chase Amazon CL to it and am closing the Amazon. The Freedom's not my highest limit card and knowing Chase it'll never be any higher, but at least now it's in the same league as my other cards, which never would have happened if I had waited for Chase.