Amex I don't have any experience with, but for Discover there really isn't a set technique or tip for getting them to open up. They can be very generous to some people and stingy with others. If you have high usage or low usage, if they're your daily driver or just get maintenance swipes, they may or may not grant a CLI. I think the best you can really do with them is use their card in whatever way is normal for you, keep working on improving your credit profile, and request CLI's as regularly as you feel like bothering with it. With regards to your credit profile, you say you have "so many inquiries" on your reports, so, depending on how many it is on the one they're SPing, that may be keeping them tight due to the appearance of credit-seeking. Letting them age may help your chances.
Does Amex give you specific reason codes, other than just saying it's your score? For Discover, it sounds like you at least need to garden for a while to let your inq's, new accounts, and derogs age. Depending on what kind of derogs you have, you could also look at trying to address them with a goodwill campaign while you wait. Unsecuring your card and giving you a CLI likely have different UW criteria, so it's not strange that they would do one but not the other, even if your scores have improved.
Paid charge-offs still count as "serious delinquency" as far as reason codes go. You don't owe on a defaulted trade line any more, but that the account got to that status is still on your reports. I don't think there's really anything you can do with paid charge-offs other than let them age, so it looks like gardening really is the main thing you need to do. You said the charge-offs are five years old so, if you don't have any other derogs, that reason code should be gone in two years. Codes for inquiries and new accounts should disappear sooner if you wait a year from your most recent app before apping for anything else.