Can`t really understand the issue. In this constellation I would book via my TA every time.
Personally I prefer Virtuoso as ameneties are often better and I like the personal contact. I only use FHR if Hotel isn`t member of Virtuoso or the suite I like to book comes not with Virtuoso-ameneties. Although I know 1 Hotel were the LHR-benefit (one way Airport Transfer) fits better for me than Virtuoso (30 minutes foot massage by the pool)