How to reduce surface tension of oil?
You may ease the droplets of water to "fall further down" across the oil by adding some of dishwasher into the water.

As just tested with a glass filled with some of sunflower oil, the water-dishwater droplets reaching the surface air./.oil will deform and flatten when they fall from about 30 cm above on said surface. Eventually however, cohesion and surface tension of water contracts these and they pass across the oil in droplike shape to reach the bottom of the glass where multiple water-dishwater droplets may coalesce.

Limitation:  Since dishwasher is a surfactant, however, it renders the two phases miscible in each other.  Stirring the content of this glas will distroy the bounderies of the two condensed phases.  (Which might be not your concern, though, reading "I could not find any cheap heavy compound miscible with oil [fit for this purpose]".)  It won't create you a thing similar like a "sand clock" which may be used again and again.

Addition since the original post was edited:  James Guides indeed added a good thought to the table.  Perhaps you do not need a liquid A imiscible to an other liquid B to study the fall of droplets, and you may use spheres instead.  Depending on perspective, this then is a problem of fluid mechanics (mécanique des fluides) as in applied biochemistry (e.g., here) and rheology (e.g., sphere viscosimeter).  In a steady state, the settling velocity $V_s$ may be described as

\begin{equation}
V_s = \frac{2}{9} \frac{r^2 g (\varrho_p - \varrho_l)}{\mu}
\end{equation}

with 
$r$ the Stokes radius of the particle 
$g$ earth's gravitational accleration 
$\varrho$ the densities of of the particle ($\varrho_p$), or of the liquid ($\varrho_l$), and 
$\mu$, the dynamic fluid viscosity (which depends even more on temperature, than $\varrho$).

Other than the two fields mentioned above, this relation is of importance havesting small crystals for X-ray diffraction analysis.  From there I know about documenting examples as in the screen photo below



taken for a large, a medium, or a small sphere of Teflon falling in a column of glycerol.  It equally allows to understand why you can't harvest small objects in a viscous medium from a bottom of a container with a spoon and have to resort to a fork.  (And with 2 mm of diameter, Brownian motion wont inhibit yet their settlment.)