Credit Advice

Being late twice - 3 years isn't that long ago to credit rating agencies - easily makes up a good portion of why your credit score is lower than what you want. Actually, it's still fairly high for having that on your record.

About the auto loans - they are not nearly as "boosting" to your score when they are paid off ... it's nice to have in your history, but it's not an active "installment loan"; you've completed your obligation.

If your AMEX Gold is your only credit card, and you're interested in raising your score specifically, you might want to add more cards to your portfolio, though I would advise to do it slowly, as you will decrease the average age of your accounts (especially if you don't have many). Having more accounts can boost your score to a minor degree, but having more open credit from those accounts has a larger positive effect.

Ultimately, on-time payment is one of THE most important parts of your credit score, so it's likely the "drag" here. It will naturally get better as more time passes.