I'm a travel agent with the ability to book both Virtuoso and Amex FHR rate codes, can offer some insight here.

You cannot "add" the FHR amenity package onto an existing non-FHR booking because of two things:

1) the FHR(/Virtuoso/Signature/Altour/etc) amenity packages are tied to the *rate* being paid, and are counted on their own for accounting purposes. Typically the FHR// rates match BAR, but can occasionally be above or below. Do you see how it can get messy when they're arbitrarily adding the amenities to a rate that may interfere with their ADR?

2) Amex is notoriously strict about contractual restrictions regarding the FHR + CTS program, so I would not be surprised if the suppliers are legally obligated to only offer the amenities on FHR rates. Another example, is that hotels cannot offer "guaranteed" 4pm late check-out on Virtuoso rates for example, due to a non-compete clause