The problem seems to me to be, your over driving your amplifier with bass turned up. Driving the amp high enough to clip the waves and make square waves will blow speakers.
Your solution is to get a more powerful amplifier to reproduce the strong bass you prefer without distortion. Keep in mind that amp power increase is not a linear event.
Every time you double the power of your amp, given the same speaker setup, you do not double the volume. You only increase the volume 3 decibels.
As an example, say you have a 25 watt per channel amp in your set up. If you go to 50 watts per channel, your volume goes up 3 decibels. For the next 3 decibel increase in volume, you would have to go to a 100 watt per ch amp. And for another 3 decibels, a 200 watt per ch amp would be needed.
Another aspect of volume would be your speaker setup. Good quality speakers will have in their specs, the amount of decibels the speaker will put out with 1 watt input @ 3 feet away.
Much can be gained by using more efficient speakers that can still handle the amount of power your amp puts out.
Example, say your speakers put out 80 decibels @ 1 watt. Buying a set of speakers that put out 90 decibels @ 1 watt would increase your volume over the less efficient speakers.
So in the end, a combination of more powerful amplifier, and more efficient speakers will make your music more enjoyable.
And don't worry about too much power blowing speakers. What blows good quality speakers is driving them to clipping. I've been using a set of Jbl home speakers rated at 60 watts on my home stereo for years. My amp puts out 300 watts per channel. I've never blown a speaker in about 20 years of use.
Because I make sure I never drive the speakers into clipping.
Your solution is to get a more powerful amplifier to reproduce the strong bass you prefer without distortion. Keep in mind that amp power increase is not a linear event.
Every time you double the power of your amp, given the same speaker setup, you do not double the volume. You only increase the volume 3 decibels.
As an example, say you have a 25 watt per channel amp in your set up. If you go to 50 watts per channel, your volume goes up 3 decibels. For the next 3 decibel increase in volume, you would have to go to a 100 watt per ch amp. And for another 3 decibels, a 200 watt per ch amp would be needed.
Another aspect of volume would be your speaker setup. Good quality speakers will have in their specs, the amount of decibels the speaker will put out with 1 watt input @ 3 feet away.
Much can be gained by using more efficient speakers that can still handle the amount of power your amp puts out.
Example, say your speakers put out 80 decibels @ 1 watt. Buying a set of speakers that put out 90 decibels @ 1 watt would increase your volume over the less efficient speakers.
So in the end, a combination of more powerful amplifier, and more efficient speakers will make your music more enjoyable.
And don't worry about too much power blowing speakers. What blows good quality speakers is driving them to clipping. I've been using a set of Jbl home speakers rated at 60 watts on my home stereo for years. My amp puts out 300 watts per channel. I've never blown a speaker in about 20 years of use.
Because I make sure I never drive the speakers into clipping.