If you do not have a car, secondary is the same as primary (it just means your regular insurance pays first and then the secondary covers what's left, which is all in your case).
There is an AMEX CDP you can use which typically gets you good rates and has the very interesting perk of a 4-hour grace period, so you can rent for 28 hours and pay one day (notice that you would still pay two days for things like the liability insurance). This CDP actually works even if you do not use the AMEX to pay.
With National, AMEX gets you Executive status, which is very good (you get to pick from the Executive Aisle in airports).