Unless your AMEX carries some type of hefty Annual Fee, do not close it. And if you don't carry a balance on it, then it really doesn't matte what the APR is, moot point.
While closing the account will not remove the account from your AAoA calculations, it will still potentially impact you none for the better.
Also, the credit limit helps limit your percentage of utilization when you do use your other cards. Just use the AMEX occassionally (it's good at more places than Costco) and PIF each month so you have no interest.
If you feel the AMEX CL is hurting you (I doubt it, but possibly) then ask AMEX to reduce the CL to say $10K. Then you don't have the large CL, you keep your oldest account open, it will still help your overall utilization and is available should you have use down the road.
FYI: Having established higher CL lines of credit makes other creditors more likely to grant higher credit. Nobody wants to go first. Some high end Visa/MC cards require you to have an existing account which exceeds a certain limit as part of the qualification. You could have high enough FICO and income, but fail because existing credit is not enough to establish the higher levels.
You must show your ability to manage high CL before creditors want to grant it. Right now many lenders are just not giving the higher CL due to necessity, not necessarily because AMEX is high for you. In fact, many AMEX holders have had CLD extensively, even those with long standing perfect history. So, your AMEX actually may be a badge of honor!
ABOUT YOUR CAR LOAN: You will have ZERO problem getting a new or used car loan with 800 FICO and the length of established credit. $45k is less income, but you have less debt also, right? And the fact that you are buying used and acting conservatively shows financial discretion.