OK, back on topic for a tick.
Tickets are now on sale for 14th June from SE England to Kilgetty (nearest station to Amroth, the start of the Pembs coastal path). With the OBRC they are £20.45 for the outward journey. The earliest Paddington train I can get which earns me the full discount is the 12.45. That involves leaving Prittlewell no later than 10.52, although I would probably get the 10.32 just to give a little leeway. That would get into Swansea at 15.43 in time for the 16.00 and arrive at Kilgetty at 17.24.
I'm going to buy one with a reservation for the 12.45 from Paddington. It will seem strange buying a ticket without a cycle reservation.