From Amex FHR's T&Cs:
Payment must be made with an American Express Card in the Platinum Card member’s name. Room upgrade upon arrival is based on availability. One special program amenity per room, per stay. Special amenity restrictions vary by hotel and cannot be redeemed for cash. Platinum Card members may reserve up to two (2) additional rooms other than for their own use, inclusive of the standard amenities and negotiated rate. The member must accompany the party as a guest for which Fine Hotels & Resorts Program reservations are made.
In light of those two points, I'd say your suggestion of giving your Plat to your son might be the best option. Then hope for the best.