It's been removed from the personal Platinum site
Seems unintentional. The T&C on the IAP site clearly state that the program is open to all Platinum and Centurion cardholders.
For fun, I called Platinum Travel Service and inquired about the below sample route.
10AUG DL 4349 SEA 05:50p -> LHR 10:50a (+1)
17AUG DL 4348 LHR 01:20p -> SEA 03:00p
Delta's web site, nonrefundable: $3,766 per ticket (fare class Z)
Platinum Travel Service quote: $3,266 per ticket (fare class Z)
Delta's web site, refundable: $9,715 per ticket (fare class I)
That's a significant discount over the standard Z fare. There's a $39
per ticket booking fee, waived for Centurion cardmembers. Rep said that all bookings must be done via phone; she's not aware of any plans to make these available via their web site.
The phone rep stated that the particular discount varies by carrier and route. We didn't get into whether there's a wide deviation among discounts or whether this is typical. But at first glance it seems very promising.