So the experiment would be "confirming the speed of gravity = c, according to SR assumptions" ?
Taking nothing away from the brilliance of SR and GR theory... but could these fundamental assumptions form part of the difficulties in experimentation, mentioned above; ie gravity probes failing to reduce their errors to something meaningful, lido finding nothing, although according to the "theory" and cheque book it should've...etc... ?
Caveat: Curious layman talking here...
.......also fyi from wiki
The Speed of Gravity What the Experiments Say