High impedance headphones do not necessarily create a higher quality of sound. High impedance will give you an advantage when pairing with a source with high output impedance. If you pair a low impedance headphone with a source with high output impedance, such as the headphone output of an old speaker amp, you will create a bump in the frequency response of the headphone around the resonant frequency of the driver. Most good sources designed for low impedance headphones have very low or zero output impedance, which makes this issue of little concern when using such a source.
Some sources will output more distortion into low impedance loads, commonly tube amps, so when using such a source, high impedance headphones will have an advantage there as well. If you have a good source that was designed for use with low impedance headphones then this will likely not be of concern.
High impedance earbud drivers may be marginally more expensive to produce so that might explain some of the difference in price. However, my opinion is that it is mostly marketing hype. I'm not saying there aren't really great high impedance earbuds, there obviously are, but there are also TOTL low impedance earbuds, so its not just impedance that matters.
This link might be of interest to you.
I have taken apart both high and low impedance earbuds and looked a the drivers up close. In the drivers I examined, the driver technology was more or less identical, as far as I could tell with the naked eye anyway. The exception being the voicecoil of course. The main difference between a low and high impedance driver is that the high impedance driver uses many more wraps of thinner gauge wire in the voicecoil compared to the low impedance driver.
These very thin wires travel from the solder pads on the back of the driver magnet towards the edge of the driver, then enter a notch in the edge of the rear driver assembly, and travel along the driver membrane until they finally reach the voicecoil.
I don't know in exactly what way your earbuds are breaking, but I will say that these tiny voicecoil wires are by far the most fragile part of an earbud driver, and if you are somehow breaking these wires in a low impedance driver, you will likely break them in a high impedance driver as well because the wires are even more fragile in a high impedance driver.
Now that may not actually be your problem, but I just wanted to point out that high impedance drivers are not by design more rugged, and I would not just assume they can handle more abuse. Whether or not a driver can hold up to your level of EQ may not just be a simple matter of higher impedance = better.
In the realm of speaker drivers, I know when you stress them beyond their capabilities with too much bass, you can end up warping the voicecoil due to the heat generated in the coil. This can cause the coil to rub on the magnet and cause very audible distortion, and also lower sensitivity of the driver. This may be what is happening to you but I can't say. I don't know how often this happens with headphone drivers, and if it is the problem, I also can't say if a higher impedance voicecoil would be better.