Let's try a thought experiment. We position ourselves 1 million metres away from the event horizon of a black hole. We then feed one million metre length rods end to tail and feed them towards the black hole. We feed then towards the event horizon. As the get nearer to the event horizon they eventually become stretched due to the tidal forces. We could ultimately determine that the event horizon is more than 1 million metres away because the million rods are too long for the distance we have calculated..

First of all that's not a contraction, it's an expansion. Don't forget that tidal forces parallel to the vertical act to stretch objects in the space, not contract them. And its not a contraction of the space but material in the space. If you used a different material with a different Young's modulus then you'd get a different length. Therefore you haven't learned only about the space but about the material as well. But the stretching would also result from the weight of the material, not just due to tidal forces. So you'd get a longer distance in a flat spacetime where there are no spatial distortions at all.

In any case, if that's the way we're doing it then you'd be getting erroneous readings due to a poorly designed experiment. For example; suppose I have a tape measure made of an elastic material. I want to measure the height h of a building so I drop the tape measure down from the roof to the ground and read off the number on the tape measure where the tape measure meets the roof. However, since the tape is an elastic material it stretches so that distances between floors at lower levels are different from distances between floors at higher levels. This is a direct result of using a poorly construct tape measure. To do this correctly we can use a laser beam. We place a mirror on the ground and then we take our laser and go to the roof. We shine the laser down to hit the mirror and the come back to the photo detector and measure the time it took for the round trip, t. The time of travel tells us how tall the building is by the formula

c = 2h/t

Therefore the height of the building, ignoring relativistic effects, is h = ct/2.

Another way to do this is to use a single 1 meter long rod. First we place one end on the ground and lay the ruler flat against the building with its edge aligned vertically. We mark where the top meets the building. That's where we put the bottom of the ruler next. We then mark off where the top of the meter rod meets the building etc. We keep doing this until we get to the top of the building and perhaps we get an measurement on the last run where the top of the rod is now higher than the top of the building. We then mark off a fraction of the stick. We add up these results and have a measure of the height of the building.

This is similar to your idea. However we must choose rods which are so small in length that the amount that they stretch due to tidal forces can be ignored. Otherwise we'd have another poorly designed measurement process.

It's extremely important in physics that you don't let these flawed measurement processes get in the way of an accurate measurement.