I can confirm.
For the GEO's, the accurate clocks are at the Ground Uplink Station (GUS), not on-board the satellite. The correction message however, is formulated (and verified for safety) at the WAAS master stations (ZLA, ZDC, ZTL) and relayed to the GUS's for up-link to the various GEO's. Both the formulated message received from the WMS, and the clock timing code generated locally at the GUS is relayed via C-band signal to the GEO. The hardware on-board the satellite translates that to the L-band down link (same as GPS) for broadcast to the user (the bent pipe).
You are also correct on the orbit of AMR being the main reason for lack of ranging on that GEO. AMR will be decommissioned from the WAAS system within the year. The satellite itself (Inmarsat 4F3) will remain in service for other means, just not as part of WAAS. The new WAAS GEO (PRN 131) which is currently in on-orbit testing will replace AMR. The new GEO (Eutelsat 117 West B @ 116.8 degrees west longitude) will provide GPS ranging in addition to the correction message data link.
There is also another WAAS GEO being launched soon (SES-5), but will not come online until 2019. It too is planned to provide ranging service.
Technically speaking, the WAAS design can support GLONASS corrections as well, but the politics of that decision are another matter.