I am not convinced that gravitational time dilation is explained by light travel time. Consider this example. A long (2 light second) rod extends from a signaller to an observer. The signaller taps the end of the rod at a rate of once per second and simultaneously flashes a flash light, also at a rate of once per second. After an initial delay of 2 seconds the observer starts to see flashes of light at a rate of once per second. After a longer delay he starts to hear the tapping sound and he hears it at a rate of once per second. The sound signal has a longer delay due to the speed of sound being slower than the speed of light, but the frequency of the signals remains the same despite the differences in signal travel time. You can think of the sound clock as the clock near the black hole. The sound simulates the slow down of the light signal but the delayed transmission rate does not in itself change the frequency of the received signal. A clock low down in a gravitational field really does tick slower (than a clock higher up) and is not an artefact of light signal travel times. Signal travel time is relevant to Doppler shift when the source is moving relative to the receiver because each signal is emitted from a different place, but here we are talking about clocks that are stationary relative to the observer.
Not quite sure what you are getting at here. I was proposing only comparing the elapsed times of the clocks when they are stationary and alongside each other at the start and end of each experiment. This eliminates any light travel time difference.
<EDIT> I just thought of a better example. Let us say we had a convoy of Ferraris with cruising at 180 mph and a convoy of heavily laden trucks cruising at 18 mph down the same highway. When they pass point A the Ferraris and the trucks are seen to pass at a rate of once per second. One hundred miles further down the highway at point B we see that the Ferraris pass a second observer at a rate of once per second and the same is true for the trucks. While it is true that the trucks arrive long after the the Ferraris, the frequency of arrival is unchanged by the speed of the vehicles or in the case of gravitational time dilation, by the speed of light signals.