>> [tvf]: Secondly, whether you are aware of it or not, GR equations of
motion (as on p. 1095 of MTW) use instantaneous interactions.

> [tr]: You just proved my point that you do not distinguish between GR
and an APPROXIMATION to GR. Please note the title of that exercise is
"Many-Body system in Post-Newtonian Limit of General Relativity" [MTW
p1091]. Their usage of the word "limit" is synonymous to my usage of
"approximation".

All expansions of functions into infinite series technically
are "approximations". But because one is free to use as many terms in
the series as desired, the approximation may be made as exact as one
pleases. So the fact that equations of motion are an "approximation" is
irrelevant because the error has been made negligible.