Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
"if you look very carefully at the lawyer-friendly weasel words in the Terms & Conditions, it says somewhere that 'entire rental must be paid for with the card for coverage to be valid'."
I think you will find that the language you quoted only applies to the free LDW coverage offered by many credit cards. I suspect Amex is more than happy to take $24.95 per rental for their Premium coverage -- even on mostly free rentals -- as long as something is still charged to a registered Amex card.
A simple call to Amex should be able to confirm this. Others have previously posted that use of a free-day or dollars-off coupon does not void the Amex Premium coverage, even though such a coupon would void the free Amex coverage.
Of course, if the rental were totally free, with no taxes or ancillary fees to be charged to a registered Amex card, that would be another matter.