There is no one line answer to your question as there are several factors. You can damage speakers by exceeding their power rating or by driving the amp into distortion or clipping. When the amp starts to clip the top of the analogue waveform gets chopped off and you are feeding DC current into your speakers which will overheat the voice coils and burn them out. You can damage the crossovers as well. With the volume at 95% I would also suspect that you drove the amp into clipping. 95% volume does not mean 95% max rated power. The power that gets put to the speakers depends on the type of content in the music and also on how the speaker impedance varies with frequency. Power ratings are just averages.
It has already been explained on how to go about repairing a damaged speaker, or simply pay the shop to do the repair. How do you prevent future damage? If you insist on playing at those volume levels then you will either need more power to prevent the amp from clipping or more efficient speakers that require less power to produce the same SPL levels. Unfortunately the R-N402D does not have pre-amp outputs so you can not connect an external amplifier. You would need a more powerful streamer/amp or go with a separate streamer with pre-amp outs along with a separate amp. The sensitivity of the Monitor 300 is not low at 90dB so you would need a speaker with a fairly high sensitivity to get more SPL with the same power. For example the Klipsch R-820F has a 97dB densitivity (speakers with horns tend to have a higher sensitivity).
If you get the speakers repaired, you will simply have to play the music at lower volumes or you will surely burn them out again. If you are able to upgrade the amp or speakers, there are on-line calculators like this one
Peak SPL Calculator to estimate how much power you need to reach a certain volume. Use a decimal meter app on your phone to measure how loud you are playing the music to see what your target SPL in dB is.
I would also recommend some research on safe listening levels. There are tables for how long you can listen at certain dB before you start doing permanent hearing damage. 100W into those speakers in a small den would be quite loud and you probably shouldn't exceed 30 minutes per day at those levels, but you need to measure the SPL levels to know for certain.