Take a step back. What is your question, what is your problem, and what is your goal?
I clearly explained it all in the post. I want to improve & preserve my credit score obviously -- by improving/preserving my credit mix which amounts to 10% (or 55 points) of the FICO score. I just re-read my post and every single question I asked is related to this and every question makes sense.
The reason I asked is that you didn't provide enough information to for us to help you formulate a winning strategy. For example, bad credit can be improved by a lot relatively quickly. But it is hard to move the needle much if you have good credit. And there are different things you need to do in each case. So knowing your credit score even roughly is key to making a plan (I see you provided that later).
Another thing you didn't provide is your timeline. This is important because while you could open personal line of credit with your bank which would improve your credit mix, you would also have an inquiry on your credit report, which can cause your credit score to go DOWN. So if you want a loan in a year maybe yes, but next month no.
But now you've shared your FICO and rough goals we can figure a few things out. One is that your FICA is high enough that it will be hard to move the needle very much no matter what you do. But the good news is that it is sufficiently high that you should qualify for most all offers.
IMO, American Express cards are great, IF you travel a lot. You didn't share with us if travel was in your plans or not, but unless it is I wouldn't bother with Amex. I certainly wouldn't get one just in hopes of raising my credit score. And if your plans change in the future you may wish you get the bonus at that time. And again, there will be a credit inquiry which you probably don't want if just raising your score is your goal. Also keep in mind that too many recent inquiries is also a negative. If your goal is to churn you don't want excess cards.
Another thing to keep in mind is that counter-intuitively you can be denied if you have too much available credit. Banks want you to use their card and too much available credit is a contrary indicator. So again, that American Express card might not be helping you.
Finally, most credit card companies give you free credit reports and have simulators on their websites so you can see the effect of canceling or open a card.