Experiment design: can one actually measure the speed of non-local light in curved spacetime

Question

The equivalence principle tells us that in some local neighborhood, every free-falling observer in a general relativistic spacetime will measure the speed of light to be $c$; this literally means at a given tangent space, a light beam's 4-velocity is a null vector. Following the geodesic postulate, it will go on its merry way following a null geodesic.

But as we know, light beams once sufficiently far away in a curved spacetime will appear to travel at coordinate speeds not necessarily $c$. The canonical example is the speeds $\frac{dr}{dt}$ of radial light beams approaching zero as they near the event horizon in the Schwarzschild spacetime from the perspective of an observer at asymptotic infinity (and so when using the standard Schwarzschild coordinates).

But what practical experiment could give a value for $\frac{dr}{dt}$? One can't bounce radar signals off the beam, for example. And even then, how would $r$ values be found for the beam of light at a given $t$?

Ingredients: We have physical meaning for the $t$ coordinate as proper time for the asymptotic observer (call their worldline $\mathcal{I}$). And the $r$ coordinate gives the physical circumference for circle $t = 0, \theta = 0, r = R, \phi \in [0,2\pi)$.

Answer 1

Answer for timelike geodesics: The observer at infinity takes a flashlight that strobes at 1 Hz, points it towards them, and lets it free fall towards the black hole. Using the gravitational redshift, the $r$ coordinate of the flashlight can be deduced at many times $t_n$ where $n \in \mathbb{N}$, thus letting the far-off observer calculate a discrete approximation to $\frac{dr}{dt}$, which in this set-up is a meaningful quantity thanks to redshift.

More generally, "observing" a far-off velocity is generally a treacherous idea, as observations can only be made in a single tangent space. Special circumstances like the redshift are needed to make meaningful observations at a distance.

Regarding the original question: No, as no experiment ever devised has been able to make a one way measurement of the speed of light (cf. popular Veritasium video). One can only measure there-and-back times, which incidentally are more consequences of the curvature of spacetime than anything else (analysis of geodesic motion).